This conversion is probably sought by users that want to use certain font (.ttf) in Adobe Illustrator graphics (.ai), or perhaps use single glyph from the font for graphics.
You cannot import a font directly to Illustrator, you have to install it to your operating system so every program can access it. Once this is done you can use this new font in the program and even export individual glyphs as outlines in the drawing.
It's is worth mentioning that old versions of CorelDRAW were able to import and edit TTF fonts and it also allowed users export to AI. Newest versions of CorelDRAW no longer support this function.
If you are looking something specific, or know something related to ttf to ai conversion, please write it in the discussion below.