What app are you using?
Books (from Apple) will display and store PDF files and has similar types of features.
Open a PDF file in Books, Tap the top of the screen, you can see the various pages at the bottom or you can tap the three lines (upper left, three dots with three lines next to them) to view the table of contents. If there is no built in table of contents, it will show you all the pages so you can quick scroll through the pages. If it does have a table of contents, you can access that with the three lines or the small images of each page with the 9 little boxes (waffle pattern representing thumbnail view)
So, it's not side-by-side with the page you are on, but it does work pretty well and it really depends on how the PDF file was created and if it does, in fact, have a table of contents.
If it has the table of contents, you'll see it as text that you can tap on each section. If it doesn't have a TOC, you'll get the thumbnail view.