They're a kind of modern myth which first came about due to the abduction story of Barney and Betty Hill in 1961. Their own experience of them seems to have been cryptomnesic memory of an episode of 'The Outer Limits' broadcast about a fortnight before, so the concept of aliens of that nature precedes their experience. Later on they were strongly popularised by Whitley Strieber in his 'Communion' book, published in 1987.
The basic idea is that there are two factions of humanoid aliens involved with the human race. One is tall, blond and angelic, and are referred to as "Nordics". These are supposed to be benevolent. The other is short, grey and kind of frog-like, and are referred to as "Greys" with distinctive wide black eyes, supposedly from Zeta Reticuli. Their motives for abducting humans are that they need to extract substances from us which are essential for their health but which they have lost the ability to synthesise naturally.
It's basically a new religion which has grown into the gap caused by secularisation. People need to believe in something but have difficulties in accepting the paranormal due to scepticism, so instead their subconscious posits the existence of physical beings with similar powers to spirits, angels, demons etc.