Q:

Why do some earthquakes and volcanoes occur within plates? 

I know that volcanoes and earthquakes occur on plate margins.  But, do some of them also occur within plates?  

A:

Crustal plates are not homogeneous, uniformly continuous rock masses with uniform stresses.  They are a mixture of rock types with variable stresses and stress concentrations.  They are also discontinuous. 
There are fault zones within plates.  Some faults are active & others inactive.   When movement occurs along an active fault, usually due to in-plate localized stresses, an in-plate earthquake will occur. 
Concerning in-plate volcanoes.  These are due to geological hotspots.  These are,

thought to be fed by underlying mantle that is anomalously hot compared with the surrounding mantle.[citation needed] Their position on the Earth's surface is independent of tectonic plate boundaries.  There are two hypotheses that attempt to explain their origins.  One suggests that hotspots are due to mantle plumes that rise as thermal diapirs from the core–mantle boundary.  The other hypothesis is that lithospheric extension permits the passive rising of melt from shallow depths.