Why did the farmer get arrested?

It is explained more in the book the film is based on. Chapter 3:

Westerberg, in his mid-thirties, was brought to Carthage as a young boy by adoptive parents. A Renaissance man of the plains, he is a farmer, welder, businessman, machinist, ace mechanic, commodities speculator, licensed airplane pilot, computer programmer, electronics troubleshooter, video-game repairman. Shortly before he met McCandless, however, one of his talents had got him in trouble with the law.

Westerberg had been drawn into a scheme to build and sell “black boxes,” which illegally unscramble satellite-television transmissions, allowing people to watch encrypted cable programming without paying for it. The FBI caught wind of this, set up a sting, and arrested Westerberg. Contrite, he copped a plea to a single felony count and on October 10, 1990, some two weeks after McCandless arrived in Carthage, began serving a four-month sentence in Sioux Falls. With Westerberg in stir, there was no work at the grain elevator for McCandless, so on October 23, sooner than he might have under different circumstances, the boy left town and resumed a nomadic existence.

A Black Box is box used to pirate TV signals by accessing channels it shouldn't have, back when it was unencrypted, and then decrypting channels it shouldn't have the decryption keys for when most of it moved to encrypted signals. There are ones for Cable TV and Satellite TV.

From a 2002 article on Pay TV Piracy:

Last week, AT&T Broadband officials in Southern California used a 5-ton steamroller to crush 3,000 "black boxes" -- illegal set-top devices designed to unscramble cable TV signals -- that were seized by law enforcement officials during the last two years in the Los Angeles area.

But in the digital age, pay-TV piracy has also gone high tech, particularly for satellite TV providers. The services use set-top receivers that are able to decode digital signals beamed down from space with a device called a conditional access module, also known as a smart card. But the receivers will get signals for free with a hacked or counterfeit card.

Black Boxes for pirated TV were more common in the late 90s in the US, but really arn't around as much anymore. The Blue Boxes used by the Steves to make free calls via in-band phone control signaling predate them by decades, but yes, its the same basic idea of pirating service. Back then, you would just pay a guy to hook up your tv cable to the pole for cheap/free. Black Boxes are needed for encrypted cable that started in the 90s, or Satellite Boxes which have always needed special equipment.