Filling the frame means moving closer to the object so that nothing will be in the photo but your subject. It is a way to get rid of extra information that is not needed. By getting closer you take a picture of the object and nothing but the object to make it look more interesting. To fill the frame you have to either move closer to the subject or zoom in leaving no space at all.
Examples:
Leading lines:
Rule of thirds: original and photoshoped
Found alphabet: photoshoped
Found alphabet: original
My name in found alphabet: original and black and white