I've seen a few achievements ("Tourist" and "Explorer") that required playing a couple of "N7 Missions". What are these?
The N7 missions are special sidequests that you'll get from reading your email or speaking to Specialist Traynor, who is standing to the right of the galaxy map. These missions are:
The first of these unlocks early - shortly after you take control of the Normandy. The rest unlock slowly throughout the plot, with the next one after you've completed Priority: Sur'Kesh. Traynor will tell you about it as you approach the map after this mission has completed. I don't believe you have to speak to her - it will be an ambient conversation that updates your Journal.
You'll have to play 2, 5, and all 6 to get the three achievements "Tourist," "Explorer," and "Tour of Duty" respectively. Note that you can also get the "Tourist" achievement (along with "Explorer" and "Tour of Duty") by playing multiplayer, if that's more your speed.
N7 Missions are a collection of side-missions that you'll be notified of via messages at your private terminal as they unlock over the course of the single player campaign.
The primary notable feature is that they all take place on maps that are used in Mass Effect 3's Multiplayer mode, so they make for a nice way to familiarize yourself with them in a single player environment.