Why does neighbouring group participation increase the rate of reaction?
In neighbouring group participation (NGP), an internal nucleophile first displaces a leaving group in an intramolecular sense, forming a ring (usually 3 or 5 membered) which is then opened by the incoming nucleophile intermolecularly. 


  
  
  General mechanism of neighbouring group participation (taken from March, Advanced Organic Chemistry, 2007


In the scheme above, Z first displaces X to form a 3 membered ring, which is then opened by Y. Your question then becomes why is Z faster than Y at substituting X?

Collision

In order for the substitution to take place, the nucleophile must come into alignment with the leaving group. In a general sense, intramolecular reactions are usually faster than intermolecular since the two reacting groups are tethered together – there is no requirement that they collide in order to react. This is especially evident for intramolecular formation of 3 and 5 reasons, since those ring sizes are especially favourable. (Note that intramolecular reactions isn't always favourable, for example in macrocyclisations of large rings, where high dilution is needed to close the ring rather than getting intermolecular reactivity). 

Entropy

The reaction between the substrate and the external nucleophile Y in an intermolecular fashion is accompanied by a decrease in entropy (two molecules are becoming one in the transition state). Whilst this also happens in the intramolecular sense (the molecule is becoming more rigid), it is significantly less than in the bimolecular case. 

Its also worth pointing out that its not always 100% clear whether a molecule is reacting via an NGP type pathway, and indeed there are many cases where its been shown that both are operating at the same time, with the intra being faster than the inter, but not sufficiently rapid to prevent any direct intermolecular reaction.