However, if the frequency of the signal you're trying to recreate gets too high, then recreating the signal becomes difficult.
For instance, both signal A and B on the right line up with the sampled points, but clearly Signal A is more natural to assume, if given only the samples.
In fact, it is mathematically impossible to construct a signal past a certain frequency threshold because of this reason.
This threshold frequency is known as the Nyquist frequency, and its value is the sample rate divided by 2.