(someone) is an expert on (a topic)

Make sure to use "on" when you're telling the topic that a person is an expert on:

She's an expert on organic farming.

You can also call someone "a ___ expert", but it doesn't work with longer phrases.

Tom is a social media expert.

It would be a little strange to say "Tom is a social media marketing expert" because that's too long.

social media

"Social media" is a new term that has become popular in the last five years or so. It means web sites where users share information with each other, like Twitter, Facebook, MySpace, FourSquare, and so on.

marketing

Marketing is a part of business. It's the activity of figuring out what customers want, and finding ways to get customers to buy from you. Marketing is a subject that you can study in school:

I took a couple of Marketing classes in college.

It's also a job area:

I'm in Marketing.

And it's an activity that businesses do:

They've spent a lot of time and money marketing this new product line.