A "fee" is money that you have to pay for a service. Items that you buy have a "cost", but services and privileges often have "fees" instead. Some examples of fees are:

• legal fees
• an entry fee (to a place or to a contest)
• a registration fee
• a membership fee

An ATM fee is money that you are charged for using a cash machine. In the U.S., it's usually free to use your own bank's ATMs. But if you try to withdraw money from another bank's ATM, you'll be charged twice - once by the bank whose ATM you're using, and again by your own bank.