The term is used in both Vampire: The Masquerade and Vampire: The Requiem. It can also be used as an insult to suggest that a vampire is inexperienced, foolish or naive. The plural of childe is childer, and a vampire's childe's childe may be referred to as their grandchilde.
A newly-Embraced childe, a fledgling, remains under the guidance and dominion of their sire; consequently, the sire may be held accountable for their childe's actions during this time. In VTM this period is called the Accounting.
Vampire: The Masquerade
A vampire's childer, can be collectively referred to as its progeny, its brood, or (in older editions), its get. Due to the inflexible nature of generation, a childe will always be of a higher generation than their sire — unless the childe lowers their generation via diablerie. Likewise, the childe acquires the sire’s clan, and thus his powers, weaknesses, and often predilections.
Some clans shelter their fledglings for years or decades, like the Tremere, while others, like many Gangrel and Brujah, figure that once you’re a vampire, you’re on your own — tough shit if you can’t hack it. The Sabbat — who sometimes call their hastily-Embraced fledglings “Shovelhead” due to their bizarre Embrace rituals — are usually much more pragmatic: If the fledgling survives and does something worthwhile, she’s not a shovelhead anymore.