The term "Sample" is used to describe a method where a constantly changing input is "observed" at one instant in time. It can also be used as a noun to describe the result of sampling.
Digital audio is somewhat analogous to film or video in that it consists of a continuous series of "still images" of the constantly changing original. In the cases of film or video; the human brain processes the incoming visual information in a way that "integrates" the rapid sequence of still pictures in a manner that is perceived as motion. This is why film actually "works" with a frame rate as low as 24 frames per second.
Audio is very different in that the human brain/mind can discriminate changes at much higher frequencies. In the case of digital audio; it is the output filters of the DA converter that integrate the individual samples into a very close approximation of the original voltage waveform.
But how does the analog to digital converter "stop" a continuously changing waveform so it can measure the voltage? By using a sample and hold circuit. The sample and hold circuit is the digital audio equivalent of a movie camera's shutter, and like the constant speed of the movie camera's shutter being 24 fps; the AD converter's sample and hold circuit must take a "snapshot" of the audio waveform voltage once every sample period.
Thus; a digital audio recording is a continuous series of samples of the constantly changing analog audio input. The samples must be played back in the same order and at the same "speed" they were recorded- the sample frequency.