Upgraded traps work in the same way as the non-upgraded traps (meaning that they do not get faster or sharper), but they do a lot more damage. This makes them more effective at protecting your gem. The less health an intruder has, the less chance they have of stealing from you.

Note that while a trap is being upgraded, it will not work and your chest will be more vulnerable. To upgrade a trap, simply tap on it. Trap upgrades require gold.
You can tell the level of a trap by its look: