Getting them increases your game stats in Popularity.

Congratulations are also used as objectives in promos like the current one, which uses "congratulate one player" to gain 30 piñata points. Daily objectives also sometimes have things like "congratulate/be congratulated by 4 players."

Or it may be someone has done something nice for you and its a way of saying Thank you

I think howrse just wanted a way for players to interact with others account pages aside from the ec forums and presentations. It also opens up another ranking category (popularity), and is also linked to objectives in events or the daily objectives.

Its pretty much like saying "hey I was here!" on peoples pages.

Understood. Thank you.

Well, I think this answers my question. Thanks, all.