"Sleeve" is a reference to the tattoo's size similarity in coverage to a long shirt sleeve on an article of clothing.
Sleeve tattoos are the ones done from half to full arm. A sleeve tattoo is a large tattoo and huge commitment. It can be collection of small tattoos or it can be a whole huge tattoo, depending on the wearer.
There is difference between full arm tattoos and sleeve tattoo, a sleeve tattoo has a theme and all the tattoos in sleeve tattoos go in coordination.
Sleeve tattoos are a collaboration between a tattoo artist and customer to demonstrate a personal and unified artistic theme.