What does the number next to my username in a Showdown mean?

The number next to your username is your rating. Your rating updates after you play against other users. This rating will appear on your profile stats page and during play against other users. Your rating will start at 1400, and then you gain and lose points depending on the rating of your opponents. For example, winning against a higher-ranked opponent will gain you more points than winning against a lower-ranked opponent.