0 WHAT DOES THE EXPRESSION "MY BAD' MEAN?

"My bad" is an American English idiom which means:

1. My fault, my mistake - I'm to blame.
2. I apologize.

In other words, a way of admitting a mistake, and apologizing for that mistake, without actually apologizing. 

Manute Bol  (Oct 16, 1962 – June 19, 2010) 
with Muggsy Bogues

It was made popular by Manute Bol -  when he would throw a bad pass, he would always say, "My bad" instead of "My fault," which now all the other players say - although it was also used before his arrival in the USA. This slang term was probably originated around 1970 before the widespread use of the Internet.

It usually means "my fault", "my mistake", "I apologize" or "mea culpa". It gained popularity with urban players of streetball and then spread into mainstream popularity. 

Its use in the 1995 film Clueless greatly increased the phrase's popularity.  The film starred Alicia Silverstone and contains what seems to have been the first use of the phrase in the mainstream media. The 1994 'Green revision pages' for the movie script has a scene with Alicia Silverstone's character learning to drive:

Cher swerves - to avoid killing a person on a bicycle. Cher: "Whoops, my bad."

Source(s): wikipedia, phrases.org.uk, urbandictionary.com