form field
A form field is a box on a PDF page somebody can fill in, tick or choose from, and whose answer the file keeps.
In more detail
Each one has a name, and the name is what matters: whoever collects the returned file reads the answers back by name, without looking at the page or knowing where the box was.
A field says what it starts as, what a reset puts it back to, whether it may be left empty and whether it may be changed at all. Those are properties of the box, not of the page it sits on.
What it does on a real document
Six kinds cover the ground: a box to type in, a box to tick, a list to choose from, a set of buttons of which one stays chosen, a place reserved for a seal, and a button that does something when it is pressed.
A field can be drawn inside a table cell as easily as anywhere else, which is what turns a printed table into one somebody fills in on screen.
Where it comes from, and why
Paper forms came first, and the earliest electronic ones were pictures of them with boxes drawn on top. Naming the boxes is what turned the picture back into data.
Two ways of doing it grew up in PDF, an older one and a heavier one layered on top; the older one is the one that opens everywhere, and it is the one written here.
See it on a finished document
The rules behind this word, and the texts they are read from