A "slug" is a way of generating a valid URL, generally using data already obtained. For instance, a slug uses the title of an article to generate a URL. I advise to generate the slug by means of a function, given the title (or another piece of data), rather than setting it manually.
An example:
<title> The 46 Year Old Virgin </title>
<content> A silly comedy movie </content>
<slug> the-46-year-old-virgin </slug>
Now let's pretend that we have a Django model such as:
class Article(models.Model):
title = models.CharField(max_length=100)
content = models.TextField(max_length=1000)
slug = models.SlugField(max_length=40)
How would you reference this object with a URL and with a meaningful name? You could for instance use Article.id so the URL would look like this:
www.example.com/article/23
Or, you might want to reference the title like this:
www.example.com/article/The 46 Year Old Virgin
Since spaces aren't valid in URLs, they must be replaced by %20, which results in:
www.example.com/article/The%2046%20Year%20Old%20Virgin
Both attempts are not resulting in very meaningful, easy-to-read URL. This is better:
www.example.com/article/the-46-year-old-virgin
In this example, the-46-year-old-virgin is a slug: it is created from the title by down-casing all letters, and replacing spaces by hyphens -.
Also see the URL of this very web page for another example.