TL;DR: It isn't explained outright on the show or in the comics, but we do know that the characters often wear body armor when:

1. It is available

2. There is a good reason for wearing it.

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When we see people in body armor, and why they wear it:

The show:

Morales and T-Dog at the department store:

This is the first time anyone other than Glenn has gone into the city on a supply run. Glenn is the archetype of the "slip in, slip out" survivor, so he's wearing street clothes. The others were presumably nervous about entering Atlanta for the first time, so the two who were on security detail - T-Dog and Morales - opted to wear armor.

T-Dog, Herschel, Glenn, and Maggie at the prison:

T-Dog, Glenn, and Herschel each wear parts of the riot gear suits while clearing zombies from the prison block, possibly because there are tons of zombies and they're fighting at extremely close quarters.

Glenn and Maggie both wear armor while fighting off the Governor's first attack on the prison, because they know there will be gunfire - in other words, they don't wear armor to ward off zombies, they wear it to protect themselves from bullets.

Later, Glenn wears the riot gear again while fleeing the prison after the Governor's second and last attack, because he has to run through a herd of zombies alone while weakened from his illness.

Sasha and Glenn at the Big Box:

The prison community needed supplies and located a "Big Box" store, but found out it was full of zombies. When a party was sent to clear the building, a couple of them wore riot gear because once again, lots of zombies in close quarters.

Eugene on the road:

Abraham refuses to go on towards Terminus because he's worried about Eugene, who Abe believes is a scientist trying to cure the epidemic. Abe only agrees to continue the journey after Glenn offers to let Eugene wear the armor.

Terminus resident:

Whoever this is, he's wearing the armor he stole from Eugene, and we don't know why he is wearing it, in-universe. Out-of-universe, he's wearing it because the writers wanted Rick to see it and grow suspicious.

Soldiers from the Kingdom:

In this case, it appears that people are wearing armor simply as a matter of course while out on patrol - this simply seems to be the way they do business in the Kingdom.

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In the comics:

Various people at the prison:

They wear the armor a bit more often in the comics, but usually because they are dealing with either herds of zombies or enemy gunfire.

The Governor:

The Governor wears armor here because he's getting into a gunfight.

Kingdom Soldiers:

Again, the Kingdom apparently armors all its patrols, but we never learn why.

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Conclusion:

As I said above, in most cases people wear armor when it is available and the situation is particularly dangerous. Their behavioral patterns indicate that they only deem armor worthwhile when they expect one or more of the following:

• Incoming gunfire
• Large numbers of zombies
• Tight quarters

The only possible exception to this is patrols from the Kingdom, who tend to wear it at all times.

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Why not wear body armor more often?

I can think of a few reasons:

1. It isn't available.

2. In most cases, it is safer to rely on speed and agility (our clear advantages over zombies) rather than tough armor that reduces speed and agility. As Max Brooks says in The Zombie Survival Guide:

Speed and agility should be your first defense against the walking dead. Armor will not only decrease both these advantages that you have over zombies, but it will also sap your energy during prolonged conflict. Add the risk of dehydration, and the prospect seems even less attractive. One final, less obvious disadvantage to annor is not physical but psychological: People wearing protective garb tend to feel more confident and therefore take greater risks than those in simple clothing. This artificial bravery has resulted in too many senseless deaths. Simply put, the best protection from a zombie bite is distance. If for some reason you insist on some type of protective gear, the following summary will provide all the information necessary for prudent decision-making...

Cold, hard figures have shown that when battling the living dead, nothing has saved more victims than basic, tight clothing and closely cropped hair. The simple fact is that ghouls attack by reaching out to grab their victims, pulling them in, then biting. Logic dictates that the less material a person offers up for grabs, the better his or her chances will be. Baggy clothing, complete with pockets, straps, or anything that might hang freely, will be a convenient handle for grasping zombie claws. Anyone who has worked in factories or with some kind of heavy machinery will tell yon the importance of never letting anything hang loose. Tight clothing, obviously within comfort limits, will help to eliminate this danger. Hair can be a similar hazard. Many times, victims have been seized and even dragged by their hair to a gruesome end. Tying one's hair back before a conflict may work temporarily.
- The Zombie Survival Guide, by Max Brooks

The comic books confirm this:

- The Walking Dead, Issue #25

3. The series is set in the American south, where the weather is often unbearably hot and humid. Covering yourself in thick armor would be extremely uncomfortable, and in the summer, rather dangerous.

4. In the rare case in which you find armor, there will likely be a rotten corpse - probably one who is thrashing around trying to eat you - inside of it. This creates a few problems:

   • If the body inside the armor is a zombie, it will be dangerous to deal with, as we saw in season 3, episode 1, Seed.

   • Regardless of whether the body wearing the armor is a zombie or just inanimate corpse, the armor will be so repulsive that few people would be willing to wear it. It will be drenched in rancid blood, caked in rotten viscera, and the stench of decomposing flesh and bodily fluids will be absolutely unbearable (and impossible to remove) - to say nothing of the fact that we saw a zombie's face slide off and stick to the inside of the gas mask it was wearing when Rick pulled the mask off.

Daryl and T-Dog actually discuss this:

(Daryl picks up a helmet, and walker-slime pours from it)

Daryl: I ain’t wearing this shit.

(T-Dog picks up gloves, and more foul slime oozes out)

T-Dog: We could boil them.

Daryl: Ain’t enough firewood in a whole forest, no! Besides, we’ve made it this far without them right?
- The Walking Dead, season 3, episode 1: Seed

The main reason is mobility. Any protection is going to limit their mobility to some degree. And mobility is key, especially when they come upon other humans who are not friendly.

They do.

• When fighting in close quarters (as in the prison), Rick's people have worn armour.

• Patrolmen from The Kingdom wear it while on horseback (so the armour doesn't slow them down), to inspire a sense of hope and security in their community and in outsiders with their knightly appearance (they also talk like knights as a matter of course).

• Negan wears a leather jacket, which acts as light protection against Walkers, though he probably wears it because he thinks it's cool.

Otherwise, there generally isn't a need for it, or there is, but it's not available or it's incorrectly thought unnecessary. Generally, I'd say armour is best worn either in firefights, or against a herd if you can't avoid them (so it would have been handy in The Battle of Alexandria). Neither of these scenarios happen on a regular basis for Rick's group.

As for lighter armour that they could wear without risking their mobility or dehydrating, I guess they would need to make it themselves, which presents the same roadblocks as making bullets: they would need time, the right materials and the right expertise, and it would be a lower priority than food, medical supplies, shelter, etc.