And why does downloading the whole blockchain on full wallet make it more secure than just using light wallet?
Your own hardware has verified all the blocks, plus all your addresses (and your coins) stay local to you. Using a light wallet, you are still essentially using an online wallet and have to trust others to not steal your BTC (not saying it'll happen, but I'm sure it has).
This isn't quite right. Your Bitcoins never really "stay local" - they're attached to addresses on the blockchain, and those addresses are everywhere a copy of the blockchain is.
What matters is your private keys. As long as your private keys are kept safe, your Bitcoins are safe, so you want a Bitcoin client that stores your private keys locally. MultiBit and Electrum both do this.
An online wallet that stores your private keys online (as most Bitcoin exchanges do) is higher risk, because somebody else theoretically
could access your private keys without your knowledge.