Why do it? I simply don't understand the reasoning behind the window minimise action.

so you won't use it. There are a lot of different functionality built into the GUI. I would say noone will use all of them.

Removal of visual desktop clutter. I don't usually minimize but instead swap windows using the ALT-TAB convention. What's your objection, though? Or is there an objection where this is a big deal to you?

Please, sir, it's "iconify".

Some folks only have 13" of real estate?

Some people believe that if you're not using an application, you should close it. And if it happens to be one of those programs that don't work that way so well, like they take a few seconds to start up or talk to the network (irc clients), they should be rewritten or you should pick a better program or something.

You leave it open and move to another workspace instead?

Guess he likes gnome shell... no functionality and all that.

No real objection, i advocate people to use their computers as they wish. Emerson is correct that i just switch workspaces. Before i was using a tiling window manager, i never even used to do that, i used to just open a new window and switch focus with the task manager.
I brought up the topic after accidentally minimising a window and wondering if people actually use the feature, because i don't see any functional purpose behind it. One could argue the same thing about wobbly windows, but they provide pleasing eye candy to some, minimising doesn't even do that.

Sometimes I have a lot of windows open, so I'll iconify some to reduce clutter. Sometimes I'll shade them.

I minimise windows so that I can see my conky. How else would I do it? Changing desktops would mean that opening Thuderbird, for example, would take more actions upon receiving an email.
Under Windows at work I minimise windows so that I can open icons from the desktop.
If you're a large monitor and/or you're into tiling then you may not see the need but how else can you see your desktop and a list of running applications to select from?

I use minimize certain applications frequently, others almost never.

For example, when I use VirtualBox to start a VM, I will then minimize the VirtualBox application window. I might not need it again for days or hours, so I put it in the closet, as it were. Similarly, I keep hexchat minimized, then skim through the IRC channels from time to time, as I seldom actively monitory them.

Others, such as my browser window and my Mutt terminal, are almost never minimized.

Applications I use infrequently, such as LibreOffice, I tend to close after I'm done with them.