'Shoe gazer' is a term to describe a sub-genre of alternative rock (there are many) that traces its roots to the UK in the early 1990s with the advent of subdued vocals and dreamy melodies driven by layers of fuzzy guitar and electronic accompaniment. The term 'shoe gazer' actually refers to the way that some of the musicians in these groups kind of stood and played while looking down at the floor, thus 'shoe gazing.'
The style is hard to pin down and some of these are probably not great examples. It's a little like 'post rock' which, by and large, I find monotonous and not good. I think that post rock is similar to the 1990s New Age music movement and therefore I refer to it as 'John Tesche's Revenge.' Shoe gazer also includes some brit pop, psychedelia and even techno dance music but it can differ from these which feature more bass and are more 'danceable' and have less of a dreamy quality.