A cesspit is a synonym for a cesspool, and it works the same way a cesspool works. Cesspits are commonly made by digging a large hole and placing precast concrete rings with holes on the sides into the hole, these rings are stacked on top of each other until the desired capacity is reached. On top of the rings a concrete top is placed, the top is either flat or dome shaped. A typical size for a modern cesspit is 3,000 gallons, which would be two rings and a dome top. Additionally, the dome top has an access hole for maintaining the cesspit.
There is a pipe coming from the associated building which carries waste water and dumps it into the cesspit. There is a layer of waste that floats on the top in the cesspit which slow decomposes through bacterial action. The water which enters the cesspit will slowly escape the bottom and sides of the cesspit.
Commonly today cesspits are linked together in series, with the first one functioning like a draining septic tank and sending any excessive water over to the second cesspit.