Honors courses can be a way to be in smaller classes, which leads to interactive classes (you MUST be prepared and can’t hide in the back of the lecture hall, you have to argue back and forth instead of simply listening, you have to apply the problem or build something…), better contact with professors, more involvement with the “life of the mind”, and building a relationship with classmates that is also tied to intellectual pursuits or the academic context.
It really depends on the university: some only offer one, perhaps two such classes per semester per level (ie., freshen could take 1-2 per semester, then 1-2 as sophomores), whereas excellent programs can offer upwards of 250-300 choices. Some universities use it as a “required classical canon” program whereas others don’t require anything.