How do I remove an app on iPhone?

Usually when I hold down on an app, all the apps start to wiggle and show an x in a circle on the top-left-hand-side tip of the app, to allow me to remove the app.

It's not doing that now. It either shows an animation on the screen and then nothing happens, or the app I am holding down on shows a menu.

How do I uninstall an app on iPhone?