Shortly after the events of the first opus, the SSV Normandy is on patrol in search of the Geths. But this patrol ends in a catastrophe since the SSV Normandy is attacked by an unknown vessel. During this attack, the Normandy SSV is completely destroyed, Commander Shepard is expelled into space and left for dead.
Here is the intro of the game + the summary of Mass Effect 1 and the choices that were made.
As a reminder: you had chosen a female character to be the hero of this game.
Two years after this event, Shepard is literally brought back to life by the Cerberus organization (although the details of the intervention are ellipsed to the player). The commander regains consciousness during a raid on the base of Cerberus where he was in intensive care. He met Jacob Taylor and Miranda Lawson explaining to him that his body was rebuilt at the request of the Man Trouble, leader of Cerberus, as part of the Lazare project.
Subsequently, Jacob and Miranda lead Shepard to the Troubled Man. The latter explains to him that he needs her because he would be the only one able to assemble a crew able to face the new threat that hangs over Humanity: the Harvesters. The Harvesters would, a priori, be allies of the Harvesters. This new species attacks human colonies to remove their settlers. Hence their name of Harvesters. The Interstellar Alliance (the entity representing humanity on the Council of the Citadel) ignores these kidnappings and prefers to stifle the case. Shepard is the only person who can make a difference.
Shepard will then be sent on Freedom's Progress to investigate with Miranda and Jacob. During their progression, they will fall upon an old acquaintance who seems to take an interest in the actions of the Harvesters.
To deal with this new threat, Commander Shepard must team up with Cerberus and recruit the best men in the Galaxy to form an elite team to save mankind.
The choices made by the player during the game have an impact on the third opus. For example, you can date a character but if he/she (you can date both sex) dies in Mass Effect 2, there is no way he/she will appear in Mass Effect 3.
BONUS
Zaeed Massani is a formidable bounty hunter and mercenary. Cerberus contracted Zaeed to help Commander Shepard in the mission of saving mankind. In exchange, Zaeed needs help completing another mission he had previously accepted, which is to release an Eldfell-Ashland Energy refinery from the Blue Suns control.
Zaeed is a character with violent manner, who will expect radical choices from you so that your agreement is good during the adventure.
Bonus
Kasumi Goto is the most enigmatic thief in the galaxy and has enemies everywhere, but only a few could put a name to his face. She is a master of stealth and infiltration.
Kasumi is a counterpart to the character of Zaeed even though she sometimes seems to obey her feelings just like him.