When something happens by turns, first one way and then another, it occurs alternately. You might spend a long train trip alternately gazing out the window and scrolling on your phone.
There are two ways to use this adverb: first, to mean "in an alternating pattern," or going back and forth from one thing to another. Spend a race alternately running and stopping to tie your shoes and you're probably not going to win. It also means "here's another possibility," so you might say: "I'm ordering the fish. Alternately, I'll get the fries and a salad." Alternately has a Latin root that means "to do one thing, then the other."