A Fluid website is one that does not have fixed widths set for the columns down the page. The content (the information on the page) flows across the full width of the screen of whatever device is being used to look at it.
The best way to understand the difference is to look at a few examples:
<example1 fluid> <example 2 fluid> <example 1 fixed> <example 2 fixed>
Fluid websites work really well on mobile devices with small screens – such as smartphones and tablets (iPads etc)
For that reason, usually Fluid websites have much larger text fonts, to make the text much easier to read on a small device.
When a website is not fluid, it has a “fixed width” layout. When the website is being designed, the widths of each column on the page are fixed at a certain numbers of pixels, or as a percentage of the screen size.
When a fixed width site is viewed on a large screen, the website will appear as a column down the centre and there will be some background fill colour on the outside sides of it.
This makes it easy to layout a website with sidebars that are to appear on every page for example.
Fixed width sites work best on desktop computers and often use smaller fonts.
See also: What is a Responsive Website?