Whats is the importance of Plymouth?

What's wrong after uninstalling plymouth?

Removing Plymouth also removes the display manager, e.g. lightdm and/or gdm and a little bit more. Here is a snippet of the remove command on my system:

sudo apt-get remove --simulate plymouth
[…]
The following packages will be REMOVED:
  cryptsetup gdm lightdm mountall plymouth plymouth-label plymouth-theme-ubuntu-gnome-logo plymouth-theme-ubuntu-gnome-text plymouth-theme-ubuntu-logo plymouth-theme-ubuntu-text ubuntu-desktop ubuntu-gnome-desktop unity unity-greeter unity-tweak-tool upstart
  upstart-bin
[…]

That's the reason, why you don't have a login screen anymore.

An advice to revert the mistake

You can always login on tty1 and reinstall lightdm/gdm and the other removed packages like ubuntu-desktop and upstart. An overview of the removed packages can you find in /var/log/dpkg.log. In my example I would have to reinstall

sudo apt-get install gdm lightdm ubuntu-desktop upstart ubuntu-gnome-desktop unity unity-tweak-tool

After that start your display manager, e.g.

sudo service gdm start

or

sudo systemctl start gdm

What is Plymouth?

Plymouth is an application that runs very early in the boot process (even before the root filesystem is mounted!) and provides a graphical boot animation while the boot process happens in the background.

_{Source: apt-cache show plymouth}

… and Plymouth replaces usplash.

Find more about Plymouth here.

From Wikipedia:

Plymouth is a bootsplash (a graphical representation of the boot process of the operating system) for Linux. It supports animations. It makes use of Direct Rendering Manager (DRM) and KMS driver. It gets packed into the initrd.

Besides eye-candy, Plymouth also handles user interaction during boot.