Your allies are automatically added to a shared leaderboard so you can comptete directly against each other.

On completiing a solution you can also look at solutions provided by your allies which ycan lead to further discussions.

Can't think of any other uses beyond those two.

I think it's just for fun, like "codewars", making "groups", "allies" and "wars"... I don't think there is any practical point in the allies system..

The honor system is an awesome way to measure participation in the codewars community. It would be really nice if we had an explicit ranking list relating only kata progress, would be kickass to see yourself rising up the ranks

Honor points is related to your participation in the community, i.e. creating katas, receiving upvotes, translating katas and solving katas. You can see more info here http://www.codewars.com/docs/ranking-and-honor-1

I think there isn't a search option to filter by clan. The only way I could find is viewing user profiles or seeing the followers/following list of the profiles, if a user is in a clan, it will appear in one of the list columns...

I don't know if this relates to ranking and honor but what exactly can you do with your allies? Like is there a purpose to them at all?