I went to apply material to my objects (something I’ve done several times with no hitch) but this is happening now, almost as if I’ve done applied something to it by accident. Could somebody help me?
It looks like you have doubled faces there. Either you have two objects overlapping, in which case you select one and delete it. The other possibility is you have overlapping faces in the same object; try selecting all vertices in edit mode and do Remove Doubles.
…or it could be a Normal related problem. Sorry but the size of the image is quite small. Try Ctrl+N to flip the normals.