What does it mean Ubuntu 18.04 will "support colored emojis"?
I guess you are quoting this OMG Ubuntu article.
Ubuntu (18.04) "supports colored emojis" means you'll be able to see system-wide coloured emojis out-of-the box, not just in some specific applications.
Currently in Ubuntu 17.10 or older versions you get to see coloured emojis without any extra modifications in for example, Firefox:
But the same emojis may render as simple monochromatic line drawings in other applications, e.g. gEdit:
Even though GNOME 3.26 (default in Ubuntu 17.10) supports coloured emojis, it's actually a missing feature in Ubuntu 17.10 as some necessary packages, which are
cairo v1.15.7, and a font that supports coloured emojis are missing (source).
This will be fixed in Ubuntu 18.04 and you'll be able to see coloured emojis everywhere out-of-the-box, as well as having a nice system picker application for choosing them.