Typography is one of the most important Web Design Elements, the industry which focuses on the readability and creativity of fonts. If you have ever designed any WordPress or Tumblr Theme, or just an HTML page, then you should have come across a point where you need to set the font family, and font sizes of different texts, titles and content.
When you design a webpage, you need to focus on everything that is on the webpage, including the images, and the text and titles. You should present all the text stuff in a consistent, clear and creative way. This is what typography is, make your text simple and attractive.
Above is short, though beautiful video and one of the best illustrations of the evolution of typography and how it appeared from white papers to the screen. I started to read and understand typography from some last years but this video, which the mentions as a Graduation Project tells everything about how it all started.
The first typography impressions on-screen were in the cinema. Beautiful serif fonts were used to show up the titles in the opening and the closing of movies and shows. There should be a balance between the different factors that make up the typography, including the text size, font, the line height etc.
And some modern fonts are trending a lot these days, like Proxima Nova( the same font this site uses in titles) and Benton Sans which can be seen on most of the blogs now. These fonts have great readability and they look creative too.