There are two causes for this, one of them is mechanical in nature, as has been described above, the modulation of the cutting stylus is able to slightly distort the wall of the adjacent groove, this can produce a faint audible signal that is synchronized to the revolutions of the disc.
However the more common cause of this "pre-echo" arises from the use of analogue tape in the preparation of the master recording for the cutting lathe. There is a phenomenon peculiar to analogue magnetic tape known as "print-through" whereby the magnetic signal impresses itself through the thin backing layer of the tape into the magnetic material of the adjacent layer. The print-through is very faint however it is audible when silence is followed by a loud section, as at the beginning of the disc, and at the start of each track. This print-through is synchronized to the revolutions of the reels of magnetic tape and usually not synchronized to the revolutions of the LP disc.
Print-through can become stronger over time, and at elevated temperatures, it is present all the way through the music, however is only noticed when there is silence followed by music. This can be prevented by the careful use of non-magnetic leader tape in the preparation of the master recording.
Print-through does not occur with the use of digital tape recording.
Technics SL1600mk2, Ortofon VMS30, modified TEAC AH500 as a preamp, Bryston 4B ST amp, Harbeth M40 speakers, all making musical magic :-)