For reference:

Be careful not to practice your righteousness in front of others to be seen by them. If you do, you will have no reward from your Father in heaven. So when you give to the needy, do not announce it with trumpets, as the hypocrites do in the synagogues and on the streets, to be honored by others. Truly I tell you, they have received their reward in full. 3 But when you give to the needy, do not let your left hand know what your right hand is doing, 4 so that your giving may be in secret. Then your Father, who sees what is done in secret, will reward you.

The explanation I heard at church was that the "hypocrites in the synagogues" would act charitable just to get the social status associated with it, but a really chariable person would want to be charitable even if they had to hide it.

I'm not completely clear on who was supposed to benefit from hiding charity. The giver, because they'd be sure they were doing good for the right reason? Or the community in general, because tolerating people who give for signalling purposes would have caused some kind of harm?

I think it's most likely that this is either virtue ethics (so the giver can be sure they're a good person), or an argument from asthetics - getting social status makes charity less asthetic.