"mi piacere" is not correct.
You could have heard "mi piace....", that is "I like...".
"Piacere" is not only a verb, but also a noun and means "pleasure".
So we say "piacere", "piacere mio", when we are introduced to someone (meaning "nice to meet you").
Or also "è (stato) un piacere", "il piacere è tutto mio", returning thanks ("my pleasure").
ciao!