Beverly Crusher's late husband and Wesley's father, a Starfleet officer who served and died under Picard's command.
Jack R. Crusher is a Starfleet officer who exists mostly in memory in The Next Generation. He was Beverly Crusher's husband and Wesley's father, and he served under Jean-Luc Picard aboard the USS Stargazer, where he was a close friend of the captain.
Jack was killed on an away mission while Wesley was still a young boy, and Picard escorted his body home to Beverly. The loss shadows Picard's relationships with both of them: it is part of what keeps him and Beverly from acting on their feelings for years, and it gives his mentoring of Wesley a personal edge. In the fourth-season episode Family, Wesley watches a holographic message his father recorded for him when he was an infant.
The name lives on in Star Trek: Picard. Beverly's son with Jean-Luc, born after the events of The Next Generation, is named Jack Crusher after her late husband, and he becomes a central character in the third season.