Why does Miss Havisham invite Pip to Satis House?
I assume you are asking about the time that Miss Havisham does this early in the book.
If that is what you are asking, I think there are two answers. The first answer is the reason that Miss Havisham actually gives at the time that she invites Pip. What she says is that she wants someone to keep Estella company -- someone young to play with her.
But it seems likely that Miss Havisham also wants someone for Estella to ensnare. She's raising Estella to break men's hearts and get revenge for her own misfortune, right? So I think she wants to give Estella someone whose heart she can break.
Specifically, she claims that she has sick fancies to see the boy play. So, he's coming over for a play date. As readers we come to know over the course of the book that Miss Havisham has a deep hatred for the male race. Part of her life's goal is to get her daughter Estella to also embody this hatred and play it out to all men. This play date with Pip gives Estella practice at making fun of men. She makes fun of him for calling Jacks knaves and for his boots. Miss Havisham is successful in meeting her goal of making Estella a man-hater. This is unfortunate, but the truth.
The correct answer why Miss Havisham wants Pip to visit her at 'Satis House' is found in Ch.7.
Mrs.Joe Gargery, Pip's sister tells her husband Joe,
`She [Miss Havisham] wants this boy [Pip] to go and play there [Satis House]. And of course he's going. And he had better play there.'
When Joe asks her how Miss Havisham came to know of Pip, she replies that Pumblechook who was a tenant of Miss Havisham recommended Pip's name to Miss Havisham when she asked him if he knew of some boy who could amuse her by coming to Satis House and play there:
Isn't it just barely possible that Uncle Pumblechook may be a tenant of hers, and that he may sometimes -- we won't say quarterly or half-yearly, for that would be requiring too much of you -- but sometimes -- go there to pay his rent? And couldn't she then ask Uncle Pumblechook if he knew of a boy to go and play there? And couldn't Uncle Pumblechook, being always considerate and thoughtful for us -- though you may not think it, Joseph,' in a tone of the deepest reproach, as if he were the most callous of nephews, `then mention this boy, standing Prancing here' -- which I solemnly declare I was not doing -- `that I have for ever been a willing slave to?'