What are the clippers number, and what do they represent ?

Clippers are similar to Trimmers but they are designed to cut large chunks of hair quickly. The clips refer to the size of the guard on the clippers. The clips are considered as ‘gatekeepers’ of how long/short your hair is. There are about 9 different sizes. From 0 to 8.

#0 (1/16 inch): closest to the skin, gets very short hair, but not bald.
#1 (1/8 inch): Short look. Ideal for Buzz cuts. Not recommended if you don’t want your scalp to show.
#2 (1/4 inch): Scalp covered. One of the most popular size for a fade haircut.
#3 (3/8 inch): Longest clip guard ordered if you want short faded sides.
#4 (1/2 inch): Medium length.
#5 (5/8 inch): Used for taper styling.
#6 (3/4 inch): Used for taper styling.
#7 (7/8 inch): Style a crew cut for thick hair. But remember to take a shorter clip guard for the sides, to fade your hair.
#8 (1 inch): Longest clipper size. Not commonly used for a fade haircut, but for a lazy way to trim the hairs on top of your head. (Possible to use #1, #2, #3 for the sides).

Credits: https://www.menshairstylesnow.com/

Now you can impress your barber with your newly acquired knowledge !