You become as sturdy as a goat, hard to knock down but when it happens you're out, 

You gain a +1 to Constitution (To a maximum of 20)

While your health is above 50% you take half damage rounded up from all attacks

Once you fall below your health threshold you take damage as normal and have disadvantage on attack rolls and ability checks 

Explanation: By taking half damage you effectively have your full health pool before the negative effects take place, meaning that in reality once you would have died you still have 1/4 of your health to make actions with disadvantage