An interesting feature of animation (of all kinds) is the control it gives the creator over "reality". In particular, for the non-physical techniques (2D drawing, 3D CGI), the rules of the animated world are determined totally by the animator; this offers all kinds of opportunities for artists.
Playing with Scale
Once you start getting down to the small scale (say, under 5" tall), the world starts to behave differently; the interplay between viscosity and surface tension in water for example, or the ratio of surface area to volume.
Water, in particular, is notorious in VFX circles for its refusal to scale - many otherwise excellent miniature shots are marred by over-sized water droplets (see Thunderbirds for many good examples).
Conversely, films like Honey I shrunk the kids (1989), which use special effects to make the audience believe that the actors have been shrunk down, are unable to produce this effect. Animated films, on the other hand, can do it with a high degree of realism - for example, 2D animation Arrietty (2010) features "oversized" water droplets which have to be squeezed rather than poured out of a kettle.
Another effect of being small can be time dilation - because the distance from the eyes to the brain is much smaller, reaction times are quicker (which is one of the reasons it's so hard to swat a fly). Although it's fairly easy to do this using VFX for a live-action film, it becomes a lot harder when you try to have interaction between the two "time scales" - however, the CGI animation Epic (2013) makes extensive use of this effect.
Playing with Geometry
Another option opened up by animation is the ability to experiment with Non-Euclidean Geometry*; for example, having objects appear larger when they are further away and smaller when they are nearer - Whisper of the Heart (1995), for example, features this anti-perspective, or this version of the scooby-doo door gag from the animated Teen Titans series.
* Non-Euclidean Geometry is a branch of geometry where 2 parallel lines can meet, the angles in a triangle can add up to whatever they want (rather than 180 degrees), and various other mind-melting impossibilities are an everyday occurrence.
Another set of possibilities opened up are things that would be impossible to film - for example, Orson Welles was famous for his use of extreme depth of field, particularly in Citizen Kane (1941), but even with techniques like in-camera matteing, he was still limited to what could be achieved with a physical camera. In contrast, animation almost defaults to having everything in focus; CGI in particular can give an almost infinite depth of field as standard.