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These are bids that show controls (aces/voids and kings/singletons) in the bid suits, usually used in slam explorations. The first time a suit is cue bid, it shows a first round control (Ace/void). The second time a suit is bid, a second round control (King/singleton) is shown.
If partner cue bids to show a 1st round control, and responder lacks any, responder rebids the agreed-upon suit. If the partner continues to cue bids, s/he tends to show 2nd round controls. Responder's subsequent bids therefore also are 2nd round controls.

              S: x              H: Jx              D: KJxx              C: KQxxx               S: AKx              H: AKQxxx              D: x              C: Axx  W        N       E        S                            1H P        2C      P        2H P        3H      P        4C P        4H      P        4S P        5C      P        5D  P        6H      P/O