it increases the friendship pt between you and the one you sent to by 1.
This is mostly used in VERY early game, when you have no lv 5 friend yet. This helps you and a partner get to lv 5 friend ASAP for the 5 extra Team instance runs.

There are other perks to having high lv friends but most of those aren't particularly useful/important.
There is also titles for the person who receive the most flower, but that's more of an ego thing.