Flynn was a 3 star general. He was appointed Director of the Defense Intelligence Agency under Obama. As head of the DIA he warned all American agencies about a certain Russian software company that was part of a spy wing for the Russian government. He also knew a lot about foreign affairs in that position. In 2014 Obama fired him. He immediately went to companies like that previously mentioned software company and worked for them, and several other Russian and Turkish agencies. Then he started working for the Trump campaign. After Trump was elected Flynn was appointed National Security Advisor even after Obama and the FBI warned Trump that he was a bad guy.
Less than a week into Flynn's new position Trump was warned by Sally Yates, the acting Attorney General that Flynn had lied about working for foreign countries and other secrets that led Yates to believe that Flynn was corruptible if not already corrupted. Trump fired Yates, not Flynn. two weeks later the news leaked about Flynn and the Yates warning and so once public, Trump had to fire Flynn too.
Since then it became known that flynn was heavily on the Turkish payroll and receiving money from Russian companies too. According to some leaks, it is believed that Flynn and his son were even hired for 15,000,000 by the Turkish government to kidnap someone in America and send him to Turkey although that never ended up happening. Flynn had to retroactively file that he was an agent of foreign countries even though he did not do that when getting his job as National Security Advisor under Trump, so he lied on those original papers. He also lied to the FBI during their investigations about Russia hacking and election manipulation.
Today Flynn plead guilty to lying to the FBI. This was part of a plea deal. It is believed by some that Flynn has intimate knowledge of the nefarious meddling Russia did in the US elections. Many think he might have information about Trump colluding with Russia. This is not proven yet. But for Mueller to accept this plea deal only makes sense if Flynn could be charged with much more serious crimes and that he had a bargaining chip of direct knowledge of impropriety or illegal activity by someone more senior than he was, so basically that Flynn would only be offered this sweetheart deal if he would flip on someone up the food chain. As National Security Advisor, there are only a few people higher up the food chain that Flynn would be in a position to flip on, like the President or Vice President.
EDIT: Missed a huge part. After Flynn was fired and then FBI director Comey was investigating Flynn along with other Russian/election issues, Trump asked Comey privately to not pursue Flynn. Comey did not stop. Comey was then fired.
Ok, that may have sounded like I'm rambling, sorry, thats as short as I can go on cliff notes.