An Electrolyte is a substance that forms ions in Aqueous solution. When an Acid or Base is mixed in an aqueous solution it will decompose into ions. That's why Acids and Bases are considered Electrolytes.
Example:
For acid : HCl + H2O ---> Cl + H3O(hydronium ion)
For base : NaOH + H2O ---> Na + OH + H2O
