The genus Homo arose in Africa about 2.5 million years ago, from an unknown species of Australopithecus.  Hominines tend to have larger brains, smaller teeth, and more human-like limb proportions than their ancestors, although among themselves they have a real assortment of tooth, brain, and face size.  The genus Homo contains the earliest hominids found outside of Africa: members of Homo erectus were living in western Asia between 1.8 and 1.2 million years ago, and in Europe by 800,000 years ago.  The genus Homo is famous for the greatest and most rapid increase in the ratio of brain size to body size that has ever occurred in mammalian evolution (70% in 700,000 years during the Middle Pleistocene), the earliest evidence of tools and other artifacts, the domestication of fire, and the first art and personal adornment.

N.B. Hominoids = anything closer to us than a monkey (gibbons, apes, Australopithecus and Homo).
Hominids = anything closer to us than an ape (Australopithecus and Homo only).
Hominines = just the genus Homo.

Species of Homo:

Homo rudolfensis (2.4 - 1.8 mya*)
Homo habilis (2.2 - 1.6 mya)
Homo erectus (1.8 - 0.2 mya)
Archaic Homo sapiens (800,000 - 200,000 years ago)
Homo sapiens neanderthalensis (300,000 - 30,000 years ago)
Homo sapiens sapiens (modern humans; 130,000 years ago - present)

*mya = million years ago