As noted in Monicas answer Gestation period is generally 28-31 days. It varies greatly by breed. My English lops usually go on day 29 but I have had a few that went on 30 and a few instances where they went over 31 days with the latest being 36 days(no that did not go well). Netherland dwarfs on the other hand go day 30-31. I have never had one go earlier or later. Some of the commercial breeds like M70 (a New Zealand cross for commercial production) have been selected for short cycle times to maximise their production value. A breeder friend of mine reports periods of as short as 24 days in his M70 herd.
The number of rabbits varies by several factors. First is breed. Smaller breeds tend to have smaller litters. For my netherlands my average has been 3-4 per litter with the largest being 7, though only one survived the first day and all were very small. My english lops tend to be 8-12 depending on the lines. There are definitely lines that I have noticed greater numbers from than others. My friends M70's typically have 12-16 per litter.
In a domestic setting most breeders will wait at least 60 days between breedings. This gives the doe time to recover from the stress of having the babies as well as to care for the litter. I personally give at least 90 days to allow the rabbit to fully recover. Most quality breeders will recommend no more than 3 litters in a year. Rabbits that are bred right back seem to have less healthy and lower quality litters than those that are given an opportunity to recover fully.
In the wild rabbits are not constrained like a domestic herd and breed pretty much right back so long as there is an alpha buck near by. Cottontails typically have litters of 6-10 about 6-7 times a year. Given a 50% mortality rate a breeding pair of rabbits can easily grow to to 50 in just one year. Repeat that for just 2 years and you have over 30000 rabbits provided there is food and shelter enough to support them.
The phrase arose because sailors would seed islands as they explored with rabbits. In just few years, with few predators, a half a dozen rabbits could fill a good size an island with a source of food to hunt, and this is the origin of the phrase breeding like rabbits.