Neutrino "turns into" an electron? Here: http://www.physics.usyd.edu.au/hienergy/index.php/Why_neutrinos_%22go_through_anything_and_everything%22
it mentions neutrinos turning into an electron. I also read that neutrinos are far less massive than electrons so how is this possible?
 A: The linked webpage is describing a process in which you start with one neutrino and one neutron and end up with one electron and one proton. The total energy and momentum are conserved in this process.
An isolated neurtino does not turn into an electron. That would violate charge conservation, among other things. 
The picture shown on that webpage is depicting only the first term in a series of terms that approximates the full process. (This is a common approximation method for handling otherwise-intractible calculations in quantum field theory.) The neutrino-electron-W part of the picture by itself, with just a neutrino in the initial state, doesn't correspond to any physically possible process.
A: In relativistic QFT, it is perfectly possible and routine to convert kinetic energy into mass: this is the heart and raison d'etre of High Energy Physics
The neutrino "turns" to an electron and a "virtual" W+ boson which gets absorbed by the hadronic target. In such interactions energy and momentum are conserved in these conversions, and it is kinematically quite possible to satisfy the energy/momentum/mass constraints for each real particle (neutrino and electron); for virtual particles, momentum and energy are still conserved, but the mass of the virtual particle need not obey such kinematic constraints ($E^2=p^2+m^2$, "on-shell condition"). 
To get a rough grasp of magnitudes, the neutrino mass is less than 1 eV; the electron mass $5\cdot 10^{5}$ eV; and the kinetic energy of the Bert, Ernie, and Big Bird neutrinos observed by IceCube in Antarctica is over $10^{15}$ eV.
