It is kindly wish for the others well-being. So simple, but so profoundly powerful and oftimes so difficult of realization. To help understand this, it is useful to consider the idea of the near and far enemies. Each of the divine abidings has a near enemy, which is a state which resembles the true abiding but misses it by being tinged with the defilements. It also has a far enemy, which is its polar opposite and which cannot share the same mental continuum.
Compassion is a state that is very often misunderstood.
There is nothing mawkish or sentimental about true compassion. It is the earnest wish that all beings be freed from their suffering. It can be thought of as an active love, whereas loving-kindness is a passive form. If it is tinged by sadness or pity then it isn't pure. Sympathetic joy is the wish that all beings continue to enjoy the pleasures they have attained.