When you create a sequence with CYCLE option, you are saying that when the sequence reaches its MAXVALUE, it will start over at the MINVALUE. This is not wise if using the sequence for primary key creation.
When you create a sequence with NOCYCLE option, you are saying that when the sequence reaches its MAXVALUE, it will NOT start over at the MINVALUE. This option is safest if using the sequence for primary key creation. When the sequence reaches its MAXVALUE an oracle error is thrown.