What is the increase of entropy principle?

For an isolated system (one that does not exchange matter of energy with its surroundings) entropy tends to raise.

The entire universe might be considered as an isolated system, and thus the entropy of the universe tends to rise and it never lowers.

Note that this is for isolated systems, not any systems.

A certain system might have its entropy go down, but for that it must exchange energy with its surroundings, and the entropy of the surroundings will raise. The change of entropy of the surroundings plus the change of entropy of the system (remember their signs) will always be positive.