I want to concentrate more on the technical aspects. You have to distinguish between Sleep and Hibernate. Both allow you to resume your work in a short amount of time, but both have different features and thus allow for different usage scenarios. Both allow you to resume work in a relatively short amount of time.
When your computer is sent to sleep, the majority of components of your computer are powered down. The memory is still being powered though, saving the state of your operating system for a quick resume. Running out of battery on a laptop or losing power otherwise will lose your session and unsaved work. There have also been cases where this damaged/destroyed the operating system. Due to this danger, this should probably only used on laptops supported by batteries or desktop computers hooked up to a UPS.
Hibernation saves the content of your memory to your hard drive, allowing the computer to be completely powered down and thus not wasting any energy. It also allows you to resume work at a different place, for example if you move your desktop computer to a new location or if you don't use a battery for your laptop. Since the memory content has to be read back into memory upon boot, getting the system back up and running takes longer than getting it out of sleep which is almost instantaneously.
Hibernation makes sense for people who have a lot of work going on that either can't be saved due to external circumstances or whose work setup is rather complex so that setting it up again would take an enormous amount of time. This can apply to laptop but probably mostly desktop users, since laptop users could also use sleep mode in conjunction with the laptop's battery. So hibernation makes especially sense for desktop computers which usually don't have an electric life line in form of batteries in case of a power outage.
Apparently, as is obvious from the other answers, people also use it to serve their laziness thinking it is actually a faster way of booting. I agree with the author of this question that in the days of SSDs and ever improving operating systems hibernation for such people doesn't really make sense. After all, there are benefits to rebooting such as flushing the memory to clear out memory leaks, removing rogue processes and whatnot. Saving the occasional seconds by using hibernation without a good reason will probably have detrimental effects if used over longer times.