If you read one of the pinned topics at the top of the Temple Forum, you'll see a brief essay of Mithraism followed by recommendations for reading.
In general, the cult meant different things at different times and places. But it seemed to be heavy on astrology, with Mithras acting as the soteriological element that elevated men's souls into the highest heaven.
And the old view of it being a competitor to Christianity is false. It didn't have the numbers or inclination because:
* it excluded women, half of the population
* it met in very small groups
* it was a religion for soldiers and people connected to the imperial establishment, a relatively small percentage of the population.
To be blunt, early Christianity was often at odds with Roman culture and government. Mithraism, by comparison, was a Roman cult par excellence, whose values were a deification of Romanatis, and whose members were fiercely loyal to the emperor and imperial society. Thus, while they had a few superficial things in common as far as rites and theology, they were completey different in tone as far as social values, and most likely did not try to "compete" with one another.