These were generally used before 1960. They take both used water from homes and other properties (called foul sewage) and rain water. Foul sewage is fairly constant - roughly the same amounts are generated every day, although there are peaks during the day such as at breakfast time. Rainfall is much more variable - from none at all to Noah proportions.
Combined sewers have to be able to carry a certain amount of rainfall in addition to the foul sewage but they can't be designed to cope with every possible drop of rain that may fall - otherwise you would end up with a sewer the size of the Channel Tunnel running under every road.
Instead sewers are normally designed to carry a fixed total volume of water. This is calculated by measuring the dry weather flow (dwf)- the amount of foul sewage generated on a normal day in a dry spell. This is then multiplied by three (known as three times dwf) to give the design capacity of the sewer.
But what happens if more rain falls than the sewer can carry? See combined sewer overflows.
Diagram of a combined sewer