It refers to the technologies used that make up your service: your web application language/framework depends on (is stacked on) your web server, which talks to (stacks on) a specific database flavor, and these run on (stack with) specific operating systems. So you might have a stack like this:
P PHP
M MySQL
A Apache
L Linux
to make up the LAMP stack, or like this:
C C#
S Sql Server
I IIS
W Windows
to make up a WISC (windows) stack. Other common “stacks” are WIMP (Windows, IIS, MySql, PHP) and WAMP (Windows, Apache, MySQL, PHP).
And those are just a few of the simple ones. It doesn’t even begin to take into account Oracle, Ruby, Java, Python, and numerous other options that could sit at various points. You could have a MySql running on linux serving as the database for a web app running in Windows, or a web service tier using a completely different technology set from your application tier (which might even be a desktop app).
The important thing is we often talk about whether your stack is windows-based or linux-based, and the reason it’s important is because software developers tend to build products with a specific stack in mind, or have experience working with one stack (or family of stacks) but not another. As long as you match up to their stack, the product should work as expected.