tab order
The tab order is the order the tab key walks through what a page can be visited on: its fields, its links, everything a reader can land on.
In more detail
Filling in a form on a screen, you type in one box, press the tab key, and the next box takes over. Which box that is has been decided by somebody. On paper the eye follows the layout and the question never arises; on a screen, either the document says what it wants or the program guesses.
A page can ask for the order its text reads in, for row by row across the page, or for column by column down it. A page that asks for nothing leaves each program to work it out, and two programs work it out differently — usually by taking the fields in the order they happen to be written in the file, which is the order whoever built the form added them.
What it does on a real document
A form in two columns is where it shows. With no order stated, a program going row by row takes the caret from the surname on the left straight across to the date on the right, back to the first name, across again — and whoever is filling it in gives up and reaches for the mouse. Asked for in reading order, it goes down the left column and then down the right, the way the form is meant to be read.
For anybody who does not use a mouse this is not a convenience but the only way through the page, which is why the rules on accessible documents ask that the order follow the reading order of the document rather than the accident of where each thing was drawn. A document that carries the structure of its own text gets it written for it: every page holding links or fields is given the reading order, without anybody having to ask.
Where it comes from, and why
A page could carry fields for seven years before it could say in which order to walk them: fields arrived in 1996, the order in 2003. In between, the order was whatever each program made of it, and a form that behaved on one machine misbehaved on the next.
The 2020 revision of the format added two more: walk them in the order the page lists them, or walk the fields first and everything else after. They ask for reading software new enough to know that revision, where the first three are read by everything.
See it on a finished document
The rules behind this word, and the texts they are read from