These are bids that show controls (aces and kings) in the bid suits, usually used in slam explorations. If you jump in a suit at the 4-level (sometimes at the 3-level too if that bid can't be natural), or bid a new suit after a trump has been agreed, it is cue-bid showing a control in suit. A control is how good control you have in the suit to the opposition taking tricks there. 1.control is Ace or Void, 2.Controll is king or single.
The most popular way is the Italian style, used by the famous Blue Team. A cue-bid shows either a 1. or 2. control in the suit. Normally you use some kind of ace asking convention, since cue-bids don't show how many aces are missing.
Here a cue-bid shows 1.controll. With good bidding technique you can even bid a good slam without using Blackwood or other ace asking tools. I don't know much about this style, so you have to find out about it yourself.
Always think about the consequences of your bid. Sometimes a cue-bid show extra strength and sometimes it is required. You should agree with partner of those position.