"Showing off" something means showing people something good that you have or that you did.
You can "show off" things like:
- your nice house
- your guitar-playing skill
- your very handsome boyfriend
You use the phrase like this:
I want to show off the necklace I got.
You can also use "show off" by itself:
He's always showing off.
In this case, "showing off" means acting in a way to make people impressed with you.