HTML is a logical presentation language. That means it is intended to provide structural information about text. For example, on this page, the phrase "Web Style" just above this paragraph is the title of this document. This is something a reader ought to know, and so the font is large and bold in order to draw attention to its titular role. The words that refer to the five sections of the Web Style essay, listed below, act as links to the sections themselves; the font is bold and blue to draw attention to their role as linking words. All of these are examples of style elements that serve a purpose in the structure of a document. More basic style elements include capitalizing the first word of a sentence, leaving spaces between words, using punctuation, starting a paragraph on a new line and indenting it, and so on. These style elements provide visual cues about the words to which they apply, for without them, written language would just be a long block of characters. These additions make it easier for the reader to understand a document's structure. On a very basic level, they make the document easier to read. (For more on typography, see Written Language.)
If I can be allowed just one more example, let's say I thought it was really important that you read these words. I might add an element of style to emphasise them. I can do that by adding HTML tags that physically specify how I want the words marked up (bold, italic, etc.), or I can add HTML tags that specify the purpose for which I want to make the physical changes to the words, which in this case is to emphasise them. This seems a trifling distinction, but it is becoming very important as the internet expands to include more people through a wider variety of devices.