The system that shows a decrease in entropy (disorder) is

There is no definite definition of entropy. In books, entropy is usually introduced through differential equations relating enthalpy and Gibb's free energy. However, that is an advanced explanation. For simplicity, entropy is the state of disorder. So, when the system shows a decrease in entropy, the system's molecules gets in order. For example, freezing water puts it in order because liquid water molecules are compacted into solid crystals. In relation, for a decrease in entropy, the reaction is more non-spontaneous.