Memory card slots are used primarily to add digital storage to a phone, by inserting a small plastic rectangle containing memory chips that can store files long-term. This extra memory can be used to expand the phone's storage available for photos, videos, audio files, games, and apps. The memory card can also be removed and used to transfer photos, videos, etc. to another device.
There are several different sizes and types of cards. The most common type of memory card in phones - by far - is microSD (as of 2020).
Adaptors are available for different sizes of SD cards. For example, a microSD card can be used in a full-size SD card slot with the proper adaptor.