Gerber in bridge is one of the most commonly used bridge conventions and an important slam bidding tool.
The Gerber 4♣ convention is used to ask for aces after a 1NT or 2NT bid from partner.
Gerber 4♣ is normally used directly over a notrump bid, usually with an unbalanced hand. It is useful when you think you're strong enough for slam, but just want to be sure you're not missing 2 Aces.
After the reply, you will now be in a position to decide whether or not to bid slam. If you don't have enough aces to bid slam, you can stop in 4NT. This is a natural bid.
For suit contracts, check out the Blackwood convention.
As soon as North opens the bidding, South is interested in a slam. But the 4♥ response shows 1 Ace and South has to be content with game.
This time North shows 2 Aces and South bids the slam.
You should only ask for kings if you are interested in bidding a grand slam, where you need all 13 tricks. You don't normally need all the aces and kings to bid a small slam.
The responses are the same over 5♣ as they are over 4♣, just one level higher.
Most experts only use the Gerber convention over a 1NT or 2NT bid from partner. Using Gerber after 3NT will too often take away the meaning of a natural, forcing club suit raise.
Slam bidding and asking for aces when your suit is clubs is problematic at the best of times. If your suit is clubs and you treat 4♣ as Gerber then it's hard to slow down! You can't sign off in 5♣ because that would be asking for Kings. Best you can do is sign off in 4NT and hope that partner doesn't think you're asking for aces with Blackwood.
This hand from a recent online game caused problems for those who tried to use Gerber.
For the natural bidders there was an easy path forward after 3NT from partner. 4♣ simply showed club support and gave plenty of room to explore for the best contract.