Long story short, Elliot (and Angela's) parents worked for E Corp, they both died from cancer and E Corp covered it up.
Fast forward to modern times, Elliot is a computer hacker that works for Allsafe, the company that does cyber security for E Corp. Angela works for Allsafe, then is given a job at E Corp after she discovers documents that prove they covered up those deaths.
Elliot develops a Mr. Robot personality to avenge his father's death. He (along with the help of Tyrell Wellick) hack E Corp and wipe out all their debt records, essentially making things like credit, credit cards, and money in general obsolete.
Elliot, realizing he actually made things worse, turns himself into the police for hacking his therapist's boyfriend (in season 1). White Rose gets him out of jail and tells him they're moving on to Stage 2. Elliot slowly realizes Stage 2 is his idea, and it's blowing up the building housing all the back-up debt records so E Corp (and society in general) can never recover.
While all this is going on the FBI starts investigating Tyrell and fsociety (Mr. Robot's hacker team)....they approach Angela. While that's going on The Dark Army (the hacker goons that helped fsociety in season 1) say "fukk it" and start killing off fsociety to cover up any evidence. Darlene (Elliot's sister) flips and starts helping the FBI.
Elliot tries to stop Stage 2 and is shot by Tyrell, who was given the gun by Mr. Robot and told to kill anyone that interferes with the plan....including him.
Now in season 3 Elliot is trying to fix things because what he did in season 1 basically ended the world as we know it. The Dark Army is letting him (Elliot) think he's succeeding in stopping them while secretly plotting with Mr. Robot and Angela, who both still want revenge.
I left out a gang of stuff but that's about as brief as a summary of this show can be breh.
Fred.