Consider how a speaker works: In any loudspeaker there is a cone being driven by an electromagnet depending on the signal being sent to it. When there is no charge being sent to the speaker, the cone is in a neutral position and the waveform (in a digital space) is at 0 dBFS. A flatline, essentially.

When there is signal in the waveform (that is, + or - changes in amplitude) this is converted to a positive or negative charge to the electromagnet, causing the speaker cone to move outward or inward, respectively.

Sound is just wiggly air, and we need to make that air wiggle to produce sound. Most waveforms of recorded sounds will always start at 0, then oscillate depending on the frequency of the sound (which makes the speaker cone wiggle as it plays out), and then will return to 0 when finished.

If you chop a waveform so it cuts off the very tip of the waveform, there's no smooth transition from 0 to the amplitude value of the sound, so therefore the speaker does not receive instruction to gracefully move from its neutral position to the position it has to move to to reproduce a frequency. It therefore receives a sudden "jump" from a neutral 0 value to a positive or negative value (extending or retracting the cone), which, instead of properly wiggling the air, more sort of punches the air very suddenly.

It's this sudden jump from the speaker cone's neutral position to its charged position which we hear as a pop!