[Speaking from experience, and also being a past and current owner of players and discs (although I haven't watched them in years).....] The video recording on laserdiscs was analog, as stated. The audio soundtrack was also initially analog, however, a digital audio soundtrack was added later (sometime in the 1980s) which was similar to the digital audio signal on a CD. Once digital audio tracks were added, laserdiscs contained both an analog stereo audio track as well as a digital stereo audio track, enabling a second audio program such as a running audio commentary and other features. When these discs are played back on a first-generation player, only the analog track will be heard, which means the main audio of the film on some titles cannot be played on these players, but only the audio commentary or other feature can be played. The first Star Wars laserdisc box set added audio commentaries at various parts of the disc on the analog track. This set can still be found on ebay very cheaply, by the way.
There was also an experimental format around 1991-1992 of analog video CDs, which were CDs containing up to 20 minutes of CD audio (playable on a regular CD player) as well as a music video playable only on Pioneer laserdisc players containing built-in CD players - the music video portion was analog video which cannot be played on a CD-ROM drive at all (even though the audio portion of the analog video was digital). Confusing, I know. To understand how it was possible for an analog signal to be recorded onto a laserdisc, there are technical articles on the internet available for the technically curious.