iRoot might work too for rooting your phone, it's a windows application that somewhat does '1-click rooting'.
Rooting a Android device basically gives you system level (A.K.A Super User) access to files on your device. Note that you will probably have to S-OFF your device in order to root it first.
Instructions on how to S-OFF your device are here:
Benefits of rooting usually allows:
- Installation of custom ROMs via custom recovery like ClockWorkMod, TWRP (Team-Win Recovery Project).
- Custom flashing and installation of custom kernels which can improve overall performance of the phone.
- Being able to use apps like Root Booster (I've only tested this on a device like the Samsung Galaxy S5 but not other devices like HTC.) which requires root of course to use the app.
Remember that unlocking your bootloader or S-OFF will void the warranty on your device. But your device probably doesn't have warranty if it's past 1 year so nothing much to worry about :).
Rooting by itself will not increase the performance of the phone.