Loneliness is a mood or drive your creatures feel at times when they have not been spending enough time around other creatures. Some creatures attempt to fix this by approaching other creatures, or playing with critters. Some toys also reduce loneliness.
In Creatures 3 and Docking Station, grendel genomes do not include a gene for reducing loneliness when meeting another of their own kind.(source)
Some norns don't appear to be affected by loneliness at all - particularly the Treehugger Norns. Loneliness plays an important part in maintaining good relationships in the Creatures Full of Edits. Its opposite is crowdedness, although in C1, loneliness does not cancel out crowdedness.