A carpool is a group of people who share a ride together in a car (or van or SUV). It is usually a privately owned vehicle, not a company car, and the driver picks up the other riders at their homes or at a prescribed meeting place. They then all drive to work or school (or whatever their destination) together. The riders will pitch in a certain amount of money for the gas, but overall it's cheaper for everyone involved. It's also better for the environment - if four people carpool to work instead of each driving their own cars, that's less pollution and fuel consumption.
A bus is not considered a carpool, but sometimes mothers will organize neighborhood carpools to take their children to school. This is usually done in areas where bus service isn't available, and it's too far for the children to walk to school.