What exactly is the Resistance in TFA? Why is Princess, I mean, General Leia in charge?
The official Star Wars database describes the Resistance as thus:
'A small, secretive private military force, the Resistance was founded by rebel hero Leia Organa to monitor the actions of the First Order. Most New Republic power brokers tolerate the Resistance while regarding Organa and her fighters as dead-enders with an unfortunate fixation on the past.
Organa’s cash-strapped movement relies on credits, ships and equipment quietly funneled to it from the few senators who share her concerns.
Soldiers of the Resistance are well trained and well equipped, but must rely on hit-and-run tactics when faced with the overwhelming might of the First Order.
If you have seen the movie, you would not necessarily have known this was the case however!
The Force Awakens was fairly light on explaining what the Resistance was exactly (and also the First Order).
There was some brief mentions by the characters - it was up to the viewers to work it out.
At its most basic level one simply had to accept that the Resistance were the good guys and the First Order where the bad guys in the same manner the Rebels were the good guys and the Empire were the baddies in A New Hope.
What would have helped explain things to the viewer was actually cut from the movie.
We briefly saw a character called Kor Sella just before the planet she was on in the Hosnian Prime system was blown up by the Star Killer base.
This is kind of a dramatic irony for she was a diplomatic aide to General Leia, and was sent to Hosnian Prime to petition the New Republic to increase support the Resistance, with the Starkiller Base as proof that the First Order broken the peace treaty that was settled many years before with the Empire!
So how big is the Resistance?
It's smaller than the Rebel Alliance was in Jedi!
In terms of ships, the organization has no capital vessels to call on, and its Starfighter numbers was woefully light—two squadrons, Blue and Red, with Poe Dameron in the leadership role.
Why is Princess, I mean General Leia in charge?
Cos it's Star Wars baby!