The acidity of nitrophenols (or any acid for that matter) is determined by the stability of the conjugate base. In the case of m-nitrophenol, the relative stability can be determined by looking at the resonance structures.
In the case of m-nitrophenol negative charge is not delocalised onto the oxygens of the nitro group and hence stabilisation is not possible in this case because there is no opportunity via resonance for delocalisation onto the nitro group.
So, meta nitrophenol is weaker acid.
