A slug is usually the title of your page, post, category, or tag, all lowercase separated by dashes rather than spaces. You can see it in the URL (web address) for this article:
support.grongtech.com.au/what-is-a-slug/
The slug is the part you see after the domain name:
what-is-a-slug
If you are having troubles with a slug being flagged as too long, check out this article for a more in-depth explanation.