The four immeasurables (appamanna), also called the divine abodes (brahmavihara), are loving-kindness, compassion, sympathetic joy and equanimity. They are "immeasurable" because they are cultivated without limit of object, extended to all beings without exception, and "divine abodes" because to dwell in them is said to be to dwell as the gods of the Brahma world dwell.
Metta, loving-kindness: the wish that beings be well and happy. Its classical text is the Metta Sutta, with its image of a mother protecting her only child and its instruction to radiate the attitude in every direction without obstruction or enmity.
Karuna, compassion: the wish that beings be free of suffering, described as the trembling of the heart at another's pain.
Mudita, sympathetic or appreciative joy: gladness at another's good fortune. It is the least familiar of the four in Western moral vocabulary, which has a widely used word for its opposite, the German Schadenfreude, and no ordinary word for the thing itself.
Upekkha, equanimity: evenness of mind toward all beings. It completes the other three rather than cancelling them, by removing the partiality and attachment that would otherwise confine them to those one already favours.
Each is taught with a "near enemy" and a "far enemy", a distinction that gives the scheme much of its practical precision. The far enemy is the obvious opposite, hatred for loving-kindness, cruelty for compassion, envy for sympathetic joy, craving or resentment for equanimity. The near enemy is the counterfeit that resembles the virtue closely enough to be mistaken for it: sentimental attachment posing as loving-kindness, pity or grief posing as compassion, and cold indifference posing as equanimity. It is the near enemies that the meditation manuals treat as the real problem. Buddhaghosa's Visuddhimagga sets out the classical method of cultivation, beginning with oneself, then a benefactor, then a neutral person, then a person one finds difficult, and finally extending in all directions without distinction.
The four are not exclusively Buddhist: they appear in Patanjali's Yoga Sutras (1.33) as the attitudes to be cultivated toward the happy, the suffering, the virtuous and the wicked respectively. In Mahayana they serve as the ground of bodhicitta, and loving-kindness practice has become one of the most widely adopted elements of Buddhist meditation in secular settings, where it has also been the subject of a substantial body of psychological research.