Consider the simple example of frequency aliasing. If you sample a 3.2MHz sine wave at a 1MHz sample rate, it looks the same as a 0.2MHz wave. But if you know a priori that the signal only has frequency components between 3 and 3.5 MHz, then you know the 0.2MHz you are measuring is actually 3.2MHz - you can fully reconstruct the original signal even though you are not sampling it fast enough.
Interestingly, in a philosophical way, you might never be able to know the “original signal”, since any signal can also technically be the alias of an infinite number of other signals, including the one used for sampling
