Ever heard of serifs? They’re the little decorative edges on typed letters of certain fonts. Times New Roman (the font in the image) is an example of a serif font. If they don’t have those decorative edges, they’re considered sans serif (without serifs). An example of a sans serif font is Helvetica.
Who might care about such a small detail on a letter?
Graphic designers care. When creating a business card or letterhead for a company, they may choose a serif font for a more classic look. If they want something more modern, they may choose a sans serif font.
Typographers care too. When creating your own typeface, you have to be consistent. One of the first decisions made by a typographer is whether or not the font will have serifs. It will determine the design of the entire alphabet (and the numbers too).