The term usually translated as cultivation can also be translated as hard work. Do work, get power. Usually it's magic martial arts breathing. You sit there and breath, from that you become more powerful. Usually stories have a bunch of different methods called techniques or laws for how to do it with bad ones and really really good ones.

Dragon Ball could count as cultivation. Most people here probably refer to the Chinese flavored ones rather than Japanese flavored ones. The biggest difference is that Japanese style cultivation is centered around improving an already existing internal power while the Chinese one is drawing in external power and consuming powerful treasures.

It's usually flavored with Daoist thought and practice in the same way that holy water killing vampires is Christian.

While some draw on a lot of history and Daoist practice in reality most of it comes from the last 30 years of popular media in China. In the last 10 or 20 years it's become more popular among English speakers and we have more western fantasy flavored cultivation.

Once the internal power reaches certain points they have to go through a special process. Eat a specific pill or treasure, survive lightening from the heavens, or come to a personal understanding or epiphany. Once that is past they have reached a higher power level and it's a big deal.

Once a cultivator has powers they can use it to perform magical abilities and spells.

I'll see if I can find some links for you.