A bound combo is a combo that involves you doing a midair combo to your opponent.
An example of a bound would be the default Combot's simple bound combo. Start off with a launcher ( + ) followed by (or depending on what side you are on) + followed by some other attacks to make it an actual combo (Like simply hitting to kick the opponent after the bound). Do this ten times.
Different characters have different ways to do launchers and bounds so experiment and see what works for you.
NOTE: This can be done in Practice Mode.