Tabinta lets you insert tab characters in multi-line text input fields. The name itself is a shorthand for "Tab in Textarea".
The default tab key behavior in Mozilla/Firefox textareas is to go to the next form field. This extension is for people who prefer inserting actual tab characters into these fields.
The itch this extension scratches is the default tab key behavior of Firefox (and other major browsers for that matter). By default the tab key navigates through links and form controls on the page. This behavior, while nice for consistency, prevents the real tab character to be entered in input fields. (Instead of inserting the character, tab key moves focus to the next field.)
Tabinta adjusts the tab key behavior; it inserts itself when pressed in a textarea; at other places it moves focus the usual way.
To read more about the problem, see Mozilla bug #29086 and a Wiki page for tab typing tips.