pH has no unit because it is a logarithmic value of H+ions
Concentration itself does have units, but pH really only looks at the power (or exponent) of the concentrations. And, for that reason the unit doesn't carry.
For example:
pH = - log [H30+] (mathematical definition) = negative logarithm of the hydronium ion concentration.
What this means is that if a solution has a concentration of 10-7 M [H30+] or (0.0000001 moles per litre of the hydronium ion), the negative log of this number = 7. Therefore the pH = 7.
But it's not 7 moles per litre or 7 moles or any other transferable unit. It's just 7.