What is meant by "Dying is the day worth living for"?

Most days of our lives are spent selfishly trying to survive (it's an overstatement, but so is Barbossa's quote). But the day where you give up your life for a greater cause, is the day you find your true purpose.

E.g. an old ex-convict saves a child from being hit by a car, but ends up getting killed himself. Even if the old ex-convict never achieved anything in his life, he made his life mean something by giving it up at a time where he could save another (more innocent) life.

If someone repeats that their previous statement is correct, you won't always believe them. If someone bets $100 on their previous statement being correct, he seems to be convinced he is telling the truth (unless he's exceedingly rich). But if someone willingly lays down his life by standing up for something, that is the most convincing way to prove that he must have believed in the ideal that he stood up for.
The cost you pay for committing to something directly affects how seriously you will be taken. And giving up your life is the biggest cost that any human can pay.

E.g. think of the buddhist monks who completely willingly set themselves on fire. They do it because they are standing up for an ideal. To preserve their culture and to stand up against what they think is wrong or evil in this world.
Doesn't that make their statement so much more powerful than if they had just all donated $50 to a charity that has the same goal?

That is the general idea that Barbossa is conveying to his men. Don't be afraid of death, but rather stand up for what you think is right because it is bigger and more important than just yourself.

Dying is the day worth living for. Because it is the day where you take a stand and refuse to lay down in the face of danger. You stand up for something that is greater than yourself. You sacrifice yourself for what you believe in. (this does exclude dying of old age, but I assume that is not common or desired among pirates anyway)

Simply put, I believe it's an original way of saying Carpe Diem ("Seize the Day.")

When you die, you will be no longer living, by definition. If "dying is the day" you live for, that would mean you live life to the fullest now, do everything you want to do now, and let Death come when it will. You live now for the day you will eventually die. To a pirate like Barbossa - a man of adventure - this is obviously preferable to living a quiet, "safe" life, fearful that death might be around every corner.

(He also knows a thing or two of which he speaks, on the subject of death, having been subjected to an undead curse in the first movie, and then gone through all that nonsense in Davy Jones' Locker - a pirate euphamism for Hell - in the second and third installments.)

It means that you shouldn't waste time waiting for something to live for tomorrow. There's a perfectly good day right here, right now that will be gone before you know it. Your life is ticking away minute by minute, don't waste it.