What is the equivalence principle of General Relativity and what does it mean?

Einstein introduced the equivalence principle by saying "We ... assume the complete physical equivalence of gravitational field and a corresponding acceleration of the reference system".

There are many ways of phrasing this but essentially what it is saying is that you can't tell the difference (or there is no difference) being in a gravitational field or 'being accelerated'. If you feel the force you feel normally standing on the Earth, you could be on the Earth ... or you could be in a rocket in deep space accelerating at 1g!

This can then be argued to imply that if you are in a freely falling reference frame, the laws of special relativity hold true for you in that frame (i.e if you are freely falling you don't feel any forces on you, 'a skydiver doesn't feel their weight').

The equivalence principle has important implications, first of all that gravity can bend light! This is the case because if you imagine a freely falling lift with a laser emitter and detector at either end of the lift, in the lift's frame of reference the light travels in a straight line from one side to the next (like in special relativity)! BUT if you change frame of reference and look from the outside into the lift, you see that the light must have travelled in an arc to leave the emitter and land at the detector. Gravity has bent the path of light!