Typography /tʌɪˈpɒɡrəfi/ - the style, arrangement, or appearance of typeset matter
>>> www.merriam-webster.com/dictionary <<<
Typography is one of the biggest part of communication. It's everywhere - on the streets (posters, signs), in stores (labels, banners), at home (newspapers, magazines, internet). It's connecting the informer with the reader indirectly on daily basis.
Big part of typography is typeface (which is nowadays mistakenly called font by a lot of people). Typeface is the single design of symbols (such as letters and numbers) - eg. Helvetica, whereas font refers to the size and weight of the typeface. Here you can learn more about the difference between typeface and font. Many people may not realize that every typeface creation needs a long designing process.
A graphic designer has endless possibilities with all the typefaces available at the moment. Most important thing is to select the proper font families and use them in appropriate way (depending on the project). While creating a layout of any kind, which includes letters, one shall not forget, that the usage of a typeface and a font varies depending on the medium - print; website; poster etc. A simple example: using weight thin or light is pointless when creating a poster, because the text wouldn't be visible from afar.
My personal favourite typefaces:
Web/digital work: Lato, Open Sans
Poster: Helvetica Neue, Museo
Book/article: Bembo MT Pro, Adobe Caslon, Adobe Garamond
If you want to learn more about the typography basics, have a look at my infographic below!