On-Ear Headphones, also called earpad or supra-aural headphones, have smaller ear pads that rest directly on the ear. In general, they do not provide the level of isolation of over-ear models, but are more convenient for wearing while out and about.
These more versatile models can offer sound quality that rivals full-size headphones. Typically, they provide a bit less isolation but that varies from model to model.
Some on-ear designs also fold into convenient travel pouches or cases. Most require no more amplification than your phone or portable player provides, but some are of sufficient quality that they will sound better if a quality amp is used. We'll note in the product description if a particular model fits this description.