one of the objectives with string theory was to unify general relativity and quantum mechanics.
now, are you aware of what special relativity is? it's just a correction you need to make to your equations involving speed, distance or time when you're dealing with things moving very fast (near the speed of light). this is for things with zero acceleration. now generalise that thought, and you get the same things, applying to things with any acceleration. this we call general relativity. now, einstein's greatest thought: if you're in a lift at some shopping centre, and the cables snap, you'll fall at 9.8m/s2 (the acceleration due to gravity). imagine the lift has no windows. you can still feel you're falling, right? now, imaginge that you're in some lift under a force that produces an acceleration of 9.8m/s2. it'd feel just the same. thus, general relativity is an explanation of gravity.
Gravity is interpreted as being the undulations of the fabric of spacetime. One of the prerequisites of GR is that this fabric is continuous (i.e. there are no holes in it).
However, quantum mechanics and GR are particle theories, and thus allow you to go down to smaller and smaller distance scales. once you reach a distance called the Planck Length, you start seeing (it's theorised) "quantum undulations". its like if you have a glass of still water, and the top of the water is the fabric of spacetime (in 2D for simplicity). if the glass is still, spacetime is nice and smooth. but shake it around and you get blobs of water bobbing up and down, and some even moving off the main body of the water itself, even though its probably for less than a second. this is what quantum undulations are. this breaking of the fabric of spacetime isn't liked by GR, and thus the pairing fails.
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