What is the /boot/efi partition and how does it affect installing a different distro

The /boot/efi system partition is simply the boot partition created when the computers mother board runs UEFI rather than BIOS as is explained here https://en.wikipedia.org/wiki/EFI_system_partition.

I do not think that the partition would be effected by installing another distro; as the installer would need to detect the motherboard firmware during the install. In order to configure the boot process if the firmware was incompatible the software should tell you and then abort the install.

I would however back up the computer first and have an Ubuntu live CD ready just in case something goes wrong. If the distro uses GRUB 2 as its boot loader (which Ubuntu does then you should not have any problems as it supports UEFI.