Funny you ask since I've recently come across a post aimed at explaining
categories and tags.
Tags are just another way to describe your content. They become another way to search for your content.
Say you wrote a post about
SEO. You describe the basics and have a section about keywords and one about links. You have sections about copywriting and site development and maybe one on analytics. So how do you categorize that post? Depends on the categories you have set up on your blog. Odds are the post would end up in a general
SEO category, but it might still be useful to someone who's only interested in researching keywords.
By tagging that same post with keyword research, link building, copywriting, etc. you allow that content to be grouped under those tags instead of just the category.
Do you have to use tags? Not at all. Whether you use them will probably depend on how you've organized your content. One thing to consider though is that each post should be in one and only one category. That same post can be tagged in as many ways as you'd like. Another consideration is that if you do categorize and tag a post it's likely accessible with two different URLs, one with the category name and one with the tag name used to find it. Odds are you'll want to keep spiders from crawling and indexing the tag versions of the page.