The <i> and <b> tags are used to specify italic and bold face, respectively. These two tags are clearly presentation specifiers. However, the <emph> tag does the same job as the <i> tag, sort of. The <emph> tag is related to the content because whatever appears between the tag and its end tag requires emphasis. This attribute (not in the same sense as attributes in a tag!) can be rendered in many ways: italic, bold, or spoken with emphasis and etc.
As a language, HTML offers both presentation tags and content tags. This is usually a bad idea, as designers can (and often do) randomly pick one type of tag to accomplish the desired visual effect. This rather arbitrary selection causes problems down the line because the wrong choice (of using <i> instead of <emph>) means that a screen reader cannot render the content with the same emphasis as the textual representation.