I dont understand exactly the quote either, maybe because it is isolated from the rest of the text but one way to see this is by observing that an electron pair in a bond is "trapped" between the two nuclei. Hence, it wont be able to expand too much in space. In contrast a lone pair is constrained only by one nucleus. Hence, it is more likely to be found further away in space compared to a bonded pair. Hence a lone pair which is nearby a bonded pair will push that bonded pair further away compared to another bonded pair. This is the reason why the H-N-H angles in NH3 are smaller than the H-C-H ones in CH4.