The simplest way to explain entropy is as the lack of differentials in a system. Suppose you start with a bucket half with cold water, half with hot water. During the first instant, the water has minimum entropy. As the heat transfers, the entropy increases. When the water has a uniform temperature, it has maximum entropy.
It doesn't have to be just temperature. It can be any property that can be transferred.
Global entropy can't decrease, but local entropy can, by increasing the entropy somewhere else.