N7 = special forces designation, the next level of training up from national special forces training. i always saw it as taking applicants from the national services' special forces be it Russian Marines, SAS or US SEAL teams, then taking these elite fighters and running them through N7 training to find the Elite of the Elite. And then the Spectre forces was taking the elite of the elite from all the races and finding the best from that group.
It should be noted that Shepard never actually went through the proper and normal process of becoming a Spectre. The Sovereign crisis followed by your death meant Shepard sort of skipped the normal training and evaluation process of the Spectre program and then there was the Reaper invasion which sort of interrupted Shepard's training again. Damn reapers.
I found that N7 was an added piece of lore that gave a little more depth to ME setting. It wasn't a key piece it wasn't a required piece but it's inclusion made the game more than it would have been. It also resonated with a lot of people as you can see N7 fan art on books, on bags and what not that isn't bioware store bought. So it seems to resonate as a symbol of ME for a lot of fans.