How Is a Signal Changed After Sampling?
First pay attention that the Nyquist Shannon Sampling Theorem requires 
sampling at rate which is strictly larger than twice (Though it is for edge cases, yet this is the accurate theorem).

Sampling is 1 step to get signals to be Discrete, which means we can store them in a digital form.
Sampling is the discretization of the Time Axis and we need to apply Quantization which is discretization of the Value Axis.

Sampling Theorem states that given a sampled signal (Which is a set of the signal values at discretized grid of time samples) what are the cases it can be fully reconstructed given a single property of the signal - Band Limited Signal.

So what's changed?
You don't have the whole signal but only set of samples from it on a time grid.