Removing the Defender
Removing the defender leaves the piece it was defending vunerable to capture.
In the diagram below the Black Knight on c6 is defending the Queen. If White captures the Queen with her Queen the Knight will capture the Queen, an equal exchange. Is there a better move?
Yes! White sees that if she first captures the Knight she will then be a whole Queen up! She plays 1.Bxc6+ and after 1...bxc6 2.Qxd4 winning the Queen!
Look at the following diagram:
Black noticed that if she played her Rook to e2 giving check to the King, when the King moves she would capture the Queen. However, at the moment the White Knight is guarding that square and would capture the Rook if it moved there immediately. Therefore the Knight has to be removed. Black plays 1...Bxf4+ (removing the Knight) and after 2.gxf4 Black can then implement her idea 2... Re2+ 3.Kd1 Rxa2