i3 is peculiar among window managers in that it is not a compositing window manager. From Wikipedia:
A compositing window manager is a window manager that provides applications with an off-screen buffer for each window. The window manager composites the window buffers into an image representing the screen and writes the result into the display memory.
i3 depends on an external application for compositing and Compton is an excellent choice if you want to improve rendering quality or apply hardware-accelerated translucency effects.
There are two issues I am aware of that affect stock compositing. One is screen tearing, which you may notice with animated effects such as Firefox's smooth scrolling. Another is a flash of partially rendered content when switching workspaces, or opening and closing windows. Using Compton should resolve those issues if it is configured correctly.
Compton also has special effects it can apply to windows such as fading and shadows. Shadows don't make much sense in a tiling window manager because windows always take up the full area of the screen, so the place where shadows would normally be rendered is off the screen.
Fading is mostly supported except for a bug with vertically split windows. The frame for the titlebars behind these windows is not transparent. The best known workaround for that is to disable titlebars with
new_window pixel. This issue might be fixed in a future release.
If you have any questions about using Compton with i3, you can ask them here on the faq.