Open Safari
Open the Bookmarks
The "Bookmarks Bar" item is there, open it.
Hit "Edit" at the top of the list.
To edit entries, hit the Entry and edit.
To move them, touch and drag the 3 lines on the right side of the list.
You are seeing History because you are in the History bookmark folder. There will be a button at the top left of the list that says Bookmarks. Tap it and you will see a list of all you BookMark folders and any bookmarks that are in the top level.
This is how you get out of any folder after you have selected it.
To get to the bookmarks that are in you header select the Bookmarks Bar folder. Now tap on Edit in the upper right corner.
You'll see your bookmarks listed with a few gadgets. The red circle with a minus sign will delete the bookmark. The three line gadget on the right can be used to drag them up and down to reorder the bookmarks.
To edit the bookmark name tap on the name. You'll be taken to another menu where you can edit the name, actual bookmark, or change the folder it is in. Just tap on the field to start editing.