Deep House is a very mature genre that was established in the mid-late 80's, though I'd like to reiterate that this guide is not an extensive history of a genre, but a look at genres in a modern context. For that reason, this guide begins in the year 2000.
The origins of Deep House had close ties with Jazz, Disco, and Soul Music, often featuring smooth vocals overlaid on top of chords from various instruments, usually either a synth or a piano. Melodic elements can regularly lean heavily on different elements of Jazz, which can lead to dissonance within pads, basslines and melodies. Though many of these traits have still carried through to modern Deep House, the genre has become much techier when compared to its roots. Deep House is typically slower compared to most other genres of house, usually sitting between 110 - 130bpm. It has a large emphasis on creating a rhythm and groove that rises and falls slowly over the duration of the track.
Mirroring wrongful classification of Progressive House vs. Big Room House, there has been a rise of popular artists that that are incorrectly classified as Deep House, e.g. Disclosure, Tchami, Oliver Heldens, etc. Rather than focusing on the groove and subtle melodies that usually pertain to Deep House, these tracks have a much stronger focus on drops with big booming basslines.