Sanity is the agent's tendency to flip out basically. In certain tense missions, sanity decreases each turn. Once it decreases enough your morale starts to go down, which in turn causes your agents to panic. I am not a master of its mechanics myself though.
Handcuffs are used so stunned enemies do not get up, but stronger enemies can break it, and you can't handcuff certain enemies like many monsters etc.
All these new mechanics are described in ufopedia though, check it out, there are a lot.