A Mimesis Training Ground is a place for a spirit master to place their martial spirit or spirit essence through an environment that emulates the natural habitat of their cor-respective spirit beast, enabling it to get the maximum results from the training. Most training ground aren't able to truly create a natural habitat because of the lack of actual spirit beasts within the grounds.
A martial spirit and a spirit beasts are basically the same. They need an environment to prey, hunt, and fight in order to grow. Only when a training ground fulfills these conditions can it be considered a full-fledged Mimesis Training Ground like the staircase below the Sea God Temple on Sea God Island.
In SL3, Shrek Academy and Tang Sect has some training grounds like this. The Spirit Ascension Platform can also be considered a Mimesis Training Ground.
In SL4, a lot of schools have these training grounds, though they are virtual.