This is a fairly good old haunted house story staring horror queen Karen Black. I got quite a kick out of all the commenters on IMDB saying "y is it called burnt offerings thers no fire in the movie lol," because as anyone with an iota of literary education can tell you, the term "burnt offerings" has nothing to do with fire. In essence, the house itself is a living entity that feeds off the energies of the people who occupy it, though you don't find this out 'til later. A young family from a busy metropolis is lured to the house for the summer by its "owners" (ghosts, manifestations, tricks of the mind, what have you) with the task of taking care of it while they're away. The caveat is that their invalid mother lives upstairs and will need to be fed everyday (and while we're giving out spoilers, "Mother Allardyce" is actually just the spirit of the house). The family ecstatically agree, and the dilapidated house immediately begins to show signs of its return to glory.
The mother from the city, Karen Black, takes the responsibility of caring for the old woman, since she was the one insisted on staying at the house due to an uncanny draw to it. The old woman never answers her door or heeds Karen's voice, but her meals are regularly eaten and Karen takes to spending a lot of time in the sitting room outside her door. She notices pictures spanning decades adorning the room, which she mistakes as family photos but are more likely portraits of the souls the house has captured.
The husband and the son are less prone to the house's influences and begin to notice the strange goings-on. The mother becomes more and more preoccupied with her charge and the house, and the great aunt they brought along for the vacation (none other than Bette Davis) fades from feisty and spry to bedridden and delusional. The family begins to find old artifacts around the grounds, which unbeknownst to them are the remains of the house's former tenants.
The husband begins to have nightmares about a raucously happy chauffeur at his mother's long ago funeral, the likes of which he hasn't had in years. These scenes came from the director's own nightmares, not from the original manuscript, and go on a little too long without any real pertinence. There are several other scenes that appear to have no meaning until the end of the movie, but these are just a little self-congratulatory and serve no purpose.
The mother's concern shifts from her family to the house and its treasures. Even after her son is nearly killed by a leaky gas pipe and the father's seeming possession in the swimming pool, she refuses to leave, stating their obligation and the fragility of old Mrs. Allardyce. When her son accidentally breaks an old relic in the house, she appears in turn-of-the-century regalia and absolutely loses her shit over it. When questioned by an increasingly worried husband, she insists and seems to believe that nothing is wrong.
The husband is now certain of the house's hold over his family, even though he doesn't fully understand it. His attempts to leave are thwarted by his wife's fervor and by the nightmares, which become real enough to appear to cross into waking life. He visits his great aunt only to find she is on her deathbed and is also having visions of the chauffeur.
The husband takes the son and tries to leave without his wife in a fit of rage, but trees fall to block their path and deal him a blow to the head that renders him immobile for a few days. His son comes close to death again in the pool, and he is finally able to convince his wife to leave. As they are going, she insists on running upstairs to tell the old lady they are going. When she doesn't return, her husband goes to the old lady's room to look for her. There's a much more iconic scene here than the one I chose but I think you can figure out what happened.
Horrified by what he's seen, the father stumbles through the window and lands on the car, which prompts the son to run screaming directly under the collapsing chimney, where the house is "shedding" its old facade and revealing a brand new exterior.
As we pull away from the photographic history of the house's vampiric tendencies, the voices of the "owners" reveal all to the viewer who may have gotten lost in the storyline (apparently to no avail, as evidenced by all the clueless IMDB forum-goers). For horror movie trivia fans out there, this house is also the exterior of the funeral home in Phantasm, a corny gem of a flick coming soon to my horror marathon photothon.