Overdubbing is a common practice in a modern studio. Considering it was not commonly used until Les Paul made innovations in multi-tracking, it is still a relatively new technology. However, it is being used in just about every recording environment imaginable today.
While it is possible to record a virtually unlimited number of tracks at the advent of digital recording technology, there used to be greater limitations. For example, there was a time when a band could only record up to 4 separate tracks. If they wanted to add more, the 4 tracks had to be bounced and mixed down to 1 track, which meant that the previous 4 tracks could not be edited anymore.
There are bands like Queen that have taken advantage of multi-tracking to an extreme. Brian May says he used to overdub something like 30 guitar tracks, and certainly their huge, layered, choral sounding vocal sounds were not accomplished without the use of multi-tracking.
There are many bands today that create their guitar sound through the use of 2 guitarists. Both guitarists use different gear, and have different playing styles, so when their 2 performances are mixed together it sounds significantly different than if only 1 guitar was playing. Some single guitarist bands have also taken advantage of this idea by recording the same guitar part twice using a different amp or different EQ setting. And you thought they got their awesome legendary tone with only one guitar performance! More often than not, that is not the case anymore. Keith Richards, for example, was said to have recorded his parts through 2 guitar amps, one dirty and one clean!
Some producers even use "digital sounds" or MIDI instruments in order to thicken up the tone of a particular instrument. For example, I have heard that some producers use a sampled sound of a snare to thicken up the existing snare sound. While it could be somewhat time consuming to accomplish this process, the end result could very well be what the band, producer, or engineer envisioned.
There are many other reasons and practical applications for multi-tracking. Suffice it to say, multi-tracking is common practice in a studio today. Simply put, it is the ability to "record over", or add additional parts to an existing recording.

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