Reactivity of meta- and para-bromo-nitrobenzene towards nucleophilic substitution
p- Bromonitrobenzene is certainly more reactive towards Nucleophilic Substitution than m-Bromonitrobenzene. The reasons are as follows,  Firstly, due to $-R$ effect of $\ce{NO2}$ group, the positive charge is created on the carbon attached to bromine in para position, which helps to increase thre electrophilicity of that carbon and that makes easier for the electrophiles to attack the benzene ring. If $\ce{NO_2}$ group would have been in  meta position, the positive charge would have been created on the adjacent carbon, so, the electrophilicity of the bromine attached carbon is not increased so much which in turn will not help it to undergo Nucleophilic attack easily. The image below demonstrates this effect on para position.  

Secondly, the Nucleophilic substitution in these systems undergo by addition-elimination mechanism. So, when the nucleophile attacks and forms the intermidiate complex, that complex is much more stabilised due to charge delocalisation in the $\ce{NO2 }$ group also if it is in para position. 

But if $\ce{NO2}$ is in meta position, the charge can only delocalise in the ring, but it can not delocalise in the $\ce{NO2}$ group (you can verify by looking at the  image also), so it is not so stabilised as the para isomer intermidiate.  These effects are mainly dominating which makes the p-Bromonitrobenzene more reactive than m-Bromonitrobenzene in Nucleophilic substitution.