As stated in other answers, Aunt Alexandra comes to stay chiefly because Tom Robinson's trial is impending and obviously it will be a tough time for the family; as Atticus puts it, 'the summer's going to be a hot one', so another adult in the family needs to be there continually for the children. This, at least, is the surface reason, but that's not all. Aunt Alexandra also feels that Scout needs a proper, guiding feminine influence in her life as she is motherless. Scout would have made do with Calpurnia, but Aunt Alexandra looks down upon Calpurnia for being both black and a servant.
Alexandra is dismayed at Scout's tomboyish ways and feels it's her sacred duty to mould her into the perfect model of a lady in every respect. As far as that goes, she appears to be fighting a losing battle from the start. However, while Scout will probably never be comfortable wearing pretty dresses and indulging in ladylike occupations like sewing, she does come to learn the importance of behaving like a lady: that is to say, being restrained, dignified,and courteous.
The perceptive young Scout guesses that Aunt Alexandra's coming to live with the family was really her idea and not Atticus's, although Atticus doesn't represent it that way:
I had an idea, however, that Aunt Alexandra’s appearance on the scene was not so much Atticus’s doing as hers. Aunty had a way of declaring What Is Best For The Family, and I suppose her coming to live with us was in that category.
Scout suspects, then, that Aunt Alexandra has more or less foisted herself upon the family, but that doesn't mean that Atticus, at least, is not grateful for her presence at a particularly testing time.
Aunt Alexandra arrives in Maycomb to help out with the children because Atticus's involvement in Tom Robinson's trial will keep him away from home working long hours. It's interesting to note the contrast in Aunt Alexandra's expectations of Scout compared with Atticus's expectations.
She is Atticus' sister, she goes to visit and live with him. She also hopes that Scout can have a maternal figure in the household since Scout's mom is not there. When she reaches she thinks that Scout is too much of a tomboy and hopes that she can be more feminine.
Aunt Alexandra comes to live in maycomb to live with her brother Atticus Finch. She wants Scout to have a mom or female figure in her life. Aunt Alexandra thinks that scout is too much of a Tomboy.