You get this Android phone, or maybe this tablet, and it has all these apps on it. Not just core stuff, like email and phone calling, but things like "AT&T Navigator," or "SprintZone," or "HTC Loves You," or "VZWConnectPlusAdvantageWireless." After you figure out (or Google) how to uninstall apps from your Android device, you drag them over to where the uninstall option should be and—nothing. Nothing happens, because you cannot uninstall some of the apps put there by the folks who made or support your phone.
There is a way to permanently remove these apps, and it involves "rooting" your phone: breaking the outer security shell that keeps you from directly accessing the deep internal functions and software inside it. Sometimes rooting can be remarkably simple, almost "one click" after downloading the right app. Sometimes it's a whole thing that requires installing nearly all the tools that an Android app maker would have. In any case, "rooting" wipes out your data, can have very unintended consequences, and is not for anyone looking to just avoid seeing ugly icons in their app list. Needing more space is another matter, but just hiding? You can usually pull that off with much less fuss.
Each phone is a little bit different, and some don't have a hiding option at all. On Galaxy phones and tablets, like the S3, the S4, and the Note 2 (and likely other Galaxy and Note things), you open the app list, tap the Menu button, choose "Hide applications," check the apps you want gone, and boom. On the HTC One in front of me (and most modern HTC devices), you open that app list, "pull down" on the list with your finger just a bit, then tap the three dots in the upper-right corner and choose "Hide apps.". In general: look for tucked-away options in the main list of apps on your phone.
But let's say your particular phone doesn't have any built-in hiding powers. What then? Well, it's time you heard about the world of alternative launchers. The "launcher" on your phone is a program, like nearly any other, that holds icons for apps, brings up a drawer with a full list of them, and creates a tidy little shortcut bar at the bottom. Google isn't the only one who makes a launcher for Android, and other launchers usually include a hiding function.
I like Nova Launcher (Free, $4 for the "pro" version that actually lets you hide apps). You install it, open it, and it imports as much as it can from your current home screen setup. The next time you hit the Home button, you're asked if you want to get there with Launcher, or Nova Launcher. Choose Nova Launcher (you can skip the "Always do this" check box if you'd like to just kick the tires a bit). Look into the Settings, under "Drawer": you'll find a nice option to "Hide Apps," which means never having to scroll through a bunch of stuff that Google, T-Mobile, or anyone else shoved on there.
Other launchers (GO, Launcher Pro, ADW) offer app hiding as well, but Nova is currently en vogue as the fastest and most complete-feeling app around. Try it out, see what it feels like, and pay a Starbucks-like price to get rid of some junk.