Enumeration means counting or reciting numbers or a numbered list. A waiter's lengthy enumeration of all the available salad dressings might seem a little hostile if he begins with a deep sigh.
When you're reciting a list of things, it's enumeration. Your enumeration of complaints about your hotel room might be received with a smile by the manager, but she may be silently engaging in her own enumeration of the reasons she doesn't want you at her hotel. The root of the word "number" — numer, from the Latin numerus — is hiding in the middle of enumeration. Just remember to leave out the b from number when you spell it.