To equip means to provide something needed for a particular purpose. If you’re planning a trip to the Arctic, you should equip yourself with warm clothes, tents, and two-way radios.
You might want to equip someone with an ice axe for ice climbing and a diving watch for underwater excursions. The ice axe or the diving watch is their equipment. Equip can also be used in a more figurative sense. If you are supposed to write computer programs but have never worked with a computer, you might say that you are not equipped for that. On a really bad day, it might feel like people are not equipped to deal with each other politely.