It really depends on what the piece is you are talking about. Some vehicles have an air dam on the bottom of the car which forces air to flow through the radiator while the vehicle is running down the road. This piece would (in its normal position) extend directly down under neath the radiator core. You'd also have a space just in front of the piece where you could see the radiator. If this is the piece, it is absolutely important. If it's not there, the car engine will run hot while you are driving at speed.
If it is just a piece which covers other parts of the bottom front side, it's not very important and can be removed if you don't mind the ugly aspect of it.
EDITED NOTE: Please note, if you remove a piece which covers vital bits/pieces (such as the radiator), it can leave these parts exposed to the elements and flying road debris. Choose wisely if the piece in question does cover any of these vital parts prior to removal.
This is one of those cases where a picture could be worth a 1000 words.