What do the dollar ($) and percentage (%) signs represent in x86 assembly?

Thats not Intel syntax, its AT&T syntax, also called GAS syntax.

the $ prefix is for immediates (constants), and the % prefix is for registers (they are required¹).

For more about AT&T syntax, see also the [att] tag wiki.

¹ Unless the noprefix option is specified, see here & here. But usually noprefix is only used with .intel_syntax noprefix, to get MASM-like syntax.