“Sure, I'll add him to the distribution list.”

You're having a phone conference with several people at work. One of the managers says that one of her employees hasn't been getting any e-mails about a certain project. She asks you to make sure that he gets these e-mails. You say:

Sure, I'll add him to the distribution list.

Sure.

"Sure" means "yes". But it's more casual. Answering "yes" to a question in a business situation is appropriate, but saying "sure" sounds more friendly.

"Sure" also has some of the meaning of "of course" - meaning that it's obvious and expected for the answer to be "yes". But "of course" is a stronger response than "sure".

I'll (do something)

You use "will" when you're announcing a decision that you just made. In this example, you heard someone say that someone wasn't getting the e-mails. So you decided to add him to the list. If you were already planning to do this, you would say:

Yes, I was going to add him to the distribution list.

add (something) to (a list)

Each point on a list is called "an item". When you make a new item for a list, you are "adding" that item to the list.

a distribution list

A "distribution list" is a list of everyone who is supposed to receive something. In e-mail, it's a convenient list of addresses for people who are supposed to get emails about a certain subject. For example, you might have a distribution list for all of the members of a department at work. Or you could create a distribution list for all of the people who are supposed to get a weekly report that you write.