Do the commendation votes at the end of of a match matter?

At the end of every Overwatch match, there are 4 players shown who did things like the most healing, most kills, most time on objective, and stuff like that. I can vote for one of these people.

What effect does my vote actually have? Does the recipient of the vote get any sort of bonus for the vote, or for having the most votes? I've won a few times but didn't notice anything special happen.

What you see is what you get! It's just an opportunity for players in the match to commend each other on good gameplay. :)
_{@PlayOverwatch on Twitter (May 30, 2016)}

Cards can reach "Epic" or "Legendary" status at 5 or 10 votes respectively. The only 'reward' is a unique voice line from the hero on the card. There's a full list of commendation voice lines on the Overwatch Wiki.

In other words, commendation votes are like clapping. They do not have any long-term tangible impact.

Right now, it's just for the lulz :D

They might add something points related in the future, who knows.