Let's take a look all the different ways this trip fits into the story:
Loose ends are tied up. I suppose Bronte could have just left the Reeds in Jane's past, but here they're dispatched with (in John Reed's case, literally).
The romantic tension moves offstage. After all their recent moments, Jane and Rochester are about to spend some time apart -- and she knows she's leaving him with Blanche. Without this physical separation, it's hard to imagine Bronte would have been able to stretch out the length of time their relationship remains unsettled.
Jane gets to explain Rochester to a stranger. And what does she tell Bessie about him?
I told her he was rather an ugly man, but quite a gentleman; and that he treated me kindly, and I was content.We get to see how Jane's grown up. Her cousins are still rather obnoxious to her, but this isn't the fly-into-a-temper Jane of the opening chapters. She's a bit above all that now.
Jane gets an honest answer to why her aunt has always hated her. Even if it's a really dumb reason, at least she knows.
A Very Important future plot point is introduced. It takes the form of a letter:
“Madam,—Will you have the goodness to send me the address of my niece, Jane Eyre, and to tell me how she is? It is my intention to write shortly and desire her to come to me at Madeira. Providence has blessed my endeavours to secure a competency; and as I am unmarried and childless, I wish to adopt her during my life, and bequeath her at my death whatever I may have to leave.—I am, Madam, &c., &c.,
“John Eyre, Madeira.”