SI:7 is most simply the premier Alliance intelligence organization, specializing in such operations as assassination, stealth tactics and special operations. Headed by Mathias Shaw out of Old Town in Stormwind City it was long considered nothing more than a front for the Stormwind Assassins another organization that Shaw also heads left to him by his Grandmother. As a result its ranks are filled primarily but not exclusively by human rogues. Human rogues will of course have a more intimate interaction with this organization as many of their rogue based quests will be handled by its members.
SI:7's history an interesting one. It actually came about as the result of Prince Anduin Wrynn seeking Shaw out and specifically requesting he create such an organization after the disappearance of King Varian. Anduin wanted an organization that was more far reaching than those already established within the human kingdoms and that would work with the other Alliance factions gathering and transporting information that others might find more difficult to accept. (Specifically the Stormwind nobility who appeared to be doing everything in their power to keep the human kingdoms from working with the others.) With the contacts he already had as a result of the Stormwind Assassins, aided by the support of Anduin and Bolvar Shaw was able to quickly to develop and implemented an organization that covered all of the Eastern Kingdoms as well as parts of Kalimdor.
Unlike its Horde counterpart all Alliance players may become aware of SI:7 due to a quest chain in the plaguelands. Here you are sent to discover what happened to some of their operatives as well as learn a little about human and forsaken hunter lore. (I won't go into details about the quest as it will spoil it.)
If you had not already guessed the name of SI:7 is considered a play on the British Directorate of Military Intelligence offices which famously go by MI5 and MI6. SI:7 would most closely resemble their MI6 branch.