Voicing a desire to "go home" is one of the most common preoccupations in people who have Alzheimer's disease. Family members and caregiving staff in nursing homes and assisted living facilities hear this question frequently, and often have trouble deciding the best way to handle it.
Often, asking to go home relates to feelings of insecurity, anxiety, or depression. Since Alzheimer's disease initially affects short-term memory, it may be that "home" reflects long-term memories of times and places that were secure and calming. One reason your mother may want to go home, even though she is already in her home, is that she is thinking of her childhood home that no longer exists.
Instead of viewing "home" as a person's usual residence, a more relevant definition may be "the place in which one's domestic affections are centered." It is this notion that is likely being expressed by many people with dementia -- the importance of domestic affections and the value of shared and loving intimacy experienced in family life. This desire to reconnect with the part of your mother's life that provided the most security, intimacy, and comfort is what she is likely expressing.
Keeping this explanation in mind, the next time your mother says she wants to go home, try to talk about and share with her those fond aspects of her childhood memories: cooking with her mother in the kitchen, playing cards or board games, playing the family piano, etc. Looking at old family and home photos together may be helpful, as may just reminiscing about her childhood home and memories.