Oooh, there’s a lot of speculation on this, even though there’s very little explicit evidence. But I’m gonna try and answer this, because this is a type of question I love to explore!

(I’m gonna go by the 1982 movie, because that’s my hyperfixation and I’m a lot less sure of myself for any of the other media.)

(And I’m going to approach this from an entirely in-universe perspective, ignoring any behind-the-scenes Doylist reasons for the colors.)

Starting with the ones that have the most canon evidence:

Blue: User-Believers, who may have been captured by MCP and forced to do various work for him, but are still loyal to the Users. This includes blue warriors like Tron, and also desk workers like Yori.

Red: those who have “renounced their belief in the Users” and joined the MCP’s “warrior elite.” How exactly they turn red is unclear, but I suspect it is not something that automatically happens when they lose their faith– instead it’s some type of ritual similar to the changing of a uniform. Flynn was able to do it by choice (well, it seemed to be part choice and part instinct) in order to disguise himself.

Purple: This shows up in the Deleted Scene– it’s really a specific sort of heliotrope/lavender color that responds to Yori’s hands as she touches Tron’s circuits. I think we can safely say that it represents Tron’s response of pleasure to her touch. (Strangely enough, we also have a few scenes suggesting that the MCP is also capable of this response.)

Yellow: The only program we see with yellow circuits is Clu, Flynn’s spyware/infiltrator/search program. I would suspect that yellow indicates the fact that he’s an infiltrator, sneaking in illicitly from outside. (This is just speculation. But it does fit with the later choice of yellow to indicate viruses, in some of the Tron videogames.)

Green: That sort of sea-green color that we see in 1982 pretty much only shows up on the MCP’s soldiers who are driving tanks. It could be the inherent circuit-color of MCP-loyal tank programs… or it could be a color-change effect that happens to any MCP soldier when operating a tank. (I tend towards the second interpretation– because we also see a somewhat similar greenish effect happen to Flynn and Ram when they’re in the Recognizer. In filming, I think this was an unintentional effect of something in that set, but in-universe I’m just gonna theorize that both tanks and Recognizers can shift the color of whoever’s in them.)

Additional notes:

Like most other things about program anatomy, I do think the meanings of circuit color can vary, depending on the individual program and the situation.

For instance, Flynn had the same color as regular User-believer programs, even though he was something distinctly different. I think the MCP chose to make him look just like the other conscripts so that he wouldn’t be treated like anything special.

And then there are the inoperative datapushers and the programs standing around in what really seems to be a red-light district, near where Flynn crashes the Recognizer. Those have a very mysterious assortment of colors, including a few shades of pink, and a red program who really does not seem affiliated with the MCP. The meaning of their colors is anyone’s guess.

Color change with emotion is also a favorite little detail. When excited in any way, the blue programs’ circuits brighten to a lighter and more brilliant blue– and Sark’s red circuits flare a sort of orange-yellow when he gets especially angry. I love those effects.