In its most basic sense, it means pushing through a crowd.
But it is also used for a more metaphorical sense. E.g. for people who don't mind pushing other people out of the way or stepping on others to get what they want.
In other words, it means to be aggressive or ambitious, usually at the expense of others.
Young employees have sharp elbows these days. They dream more about management positions and high salaries than their older colleagues.
By Emily
Sharp Elbow
1. to push somebody out of the way 2. to push your way through a crowd
1. Sarah sharpelbowed Susan when she was in the way of her talking to her boyfriend, Fred.
2. Jared sharp elbowed his way through the crowd in order to get through