"Boyfriend jeans" is a style of women's jeans that get their name from the fact that they are theoretically supposed to look like jeans that the woman wearing them "borrowed" from her boyfriend. To this end, they are somewhat looser and more comfortable than regular women's jeans, and slightly closer in cut to men's jeans.
That said, these are definitely still women's jeans, and the cut of the waist in particular is pretty much identical to any other women's jeans. However, the legs are definitely looser. These are pretty much the opposite of "skinny jeans."
The other defining feature of boyfriend jeans is that they stop at mid-shin, typically ending in a rolled-up cuff.
Boyfriend jeans are perennially popular because they have a roguish look that is much more stylish than other styles of women's jeans that emphasize comfort, such as the notorious "mom jeans" style, yet still are very easy to wear and far more comfortable than average women's jeans, and also go well together with a lot of different kinds of looks and tops.