First of all, on caveat: Honor is capped at 75% either way until Chapter 6. Some players beat themselves up trying to be saints to get it higher. Just keep that in mind.
Ok, the biggest effects that honor has is on in-game store pricing, the better your honor, the bigger your discounts.
There are two levels of high honor that unlock two of the outfits at each store where outfits are sold. You can get the higher honor one before Ch 6, you can't really tell if you are fully there unless you use a ruler on the honor bar on the screen.
At the gunsmith, there are two grips that are unlocked a capped max honor. I think one of them was supposed to be for low honor, and it's probably a glitch that they never fixed.
Honor has an effect on the loot that NPCs drop, it varies as you go extreme either way with honor.
Not directly having to do with honor level, but on some chance encounters, such as snake bite victims and hunters that trap themselves, the good honor outcome comes with a second encounter and a reward. On the hotel robbery encounter in Valentine, keeping the money you stole will get a second encounter with him. Peeping Tom encounters are entertaining if you do the bad thing and have a look for yourself.
There are a few places in the story missions where honor has an effect on the dialogue, especially the last mission of Ch 6. Super high honor and other requirements with get you an encounter with the Sister at the train station instead of Reverend Swanson at the end of another Chapter 6 mission.
Don't beat yourself up trying to shoot for high honor. It's very easy to maintain it, do hunting, donate meat to Pearson, donate to the box at camp, and this usually makes up for all the bad things you do, if you don't play like an out-of-control psychopath. Use lasso and hogtying instead of cold-blooded murder, run from the law instead of massacring them, or surrender to the law for an honor boost if you get caught.
Some real dumb advice you will see out there is throwing fish back while fishing. I do this if the fish are too small, as that is what good fishermen do, but you get more honor putting them in your satchel and donating them to Pearson back at camp. However, using greet instead of antagonize with NPCs will get you honor, but the best way to farm it is to love on dogs. They don't talk back, and don't make Arthur sound pathetic like he does when he greets NPCs too much.
In Chapter 6, there is a 1.5x honor multiplier for honor events, so it's very easy to redeem yourself if you want the high honor ending and you've been a real bad boy.