Times New Roman had its original purpose in the company of the Times. It was used as the newer typeface for printing the Times Newspaper.
It was originally designed as a letterpress typeface, and was used within offset printing. The beauty of letterpress-printing was that all the letters had a small edge which overflowed the natural forms of the letter, (click here for the letterpress print) causing it to be a bit bolder than the original cut.
This special characteristic of letterpress caused Times New Roman quite some troubles with the modern printing. Inkjet would still be do-able, because of it not being very precise, but with laser-printers the lines disappear too much. A lot of adaptations had to be made to be digitally usable.