The noun council refers to a group of people that discusses or decides about a particular subject, or that represents people, or runs an organization. It is like a committee.
The city council voted to invest more funds in education.
The security council is debating the use of armed guards at shopping centers.
The noun counsel means "advice" (especially from a knowledgeable person) and the verb counsel means to give this advice:
You need some professional counsel; you should call a lawyer.
My parents counseled me to save money and not spend it all.