What do the different shapes and colors in launcher icons mean?
When you start an app, the launcher icon pulses to let you know that Ubuntu is starting your app. This is useful because while some apps start immediately, others may take a minute to load.
Once the app has finished starting, a small white triangle will show to the left of the launcher square. Two triangles means that you two windows of the same app open. If you have three or more windows of the same app open, three triangles will show.
Apps that aren't currently running have translucent launcher icon squares. When an app is running, the launcher icon square is full of color.
If an app wants your attention to notify you of something (like a finished download), the launcher icon will wiggle and glow and the white triangle will become blue. Click the launcher icon to dismiss the notification.
Apps can also show a number on their launcher icon. Messaging apps use the number to tell you how many unread messages you have. Software Updater uses it to tell you how many updates are available.
Finally, apps can use a progress bar to let you know how long a process is taking without you needing to keep the app window in view.