"Clients" are similar to "customers". But the word "customer" suggests someone buying things at a store or directly on the Internet. The word "client" is used in business-to-business sales:
I have a meeting with a client this afternoon.
People have long meetings with their clients, take them out to lunch, and try to sell them products or services for large amounts of money. When a client buys something, they usually use their company's money, not their own personal money.
The word "client" can mean the person that you do business with, or it can also mean the company that they belong to:
Microcorp is a client of ours.