What is a wrathful Buddha?

According to the Wiki wrathful deities are representations of negative Kamma. It says that the wrathful forms of appearance is actually meant to lead beings towards enlightenment.

In Buddhism, wrathful deities are enlightened beings who take on wrathful forms in order to lead sentient beings to enlightenment. They are a notable feature of the iconography of Mahayana Buddhism and of Tibetan Buddhism, and other Vajrayana traditions in particular. A wrathful deity is often an alternative manifestation of a bodhisattva or other normally peaceful figure, making the representations of all human vices and atrocities. True to their name, in Tibetan art, wrathful deities are presented as fearsome, demonic beings adorned with human skulls and other bone ornaments.

The wrathful (or terrifying deities) are representations of negative karmas, in the same way as peaceful deities are representations of positive karmas. The symbol of the wrathful ones is the kapala, a half skull filled with blood.

This does not however answer what a wrathful Buddha is but if one follows the thought further one might suggest that the wrathful form of a Buddha might serve the same purpose as deities with wrathful appearances.

Here is another very interesting quote on Wrathful Forms:

Wrathful Forms

People who are not accustomed to the "language" of Tibetan Buddhist images are often surprised to see the wrathful deities for the first time.

One category of these is the herukas, a class of Vajrayana deities such as Chakrasamvara that is semi-wrathful with intimidating, even terrible, features. They are represented as partially nude with an upper garment of human skin and a tiger skin around their hips. They have a 5-skull headdress and carry bone rosaries, a staff or trident and a damaru (pellet drum) like the Hindu god, Shiva. Herukas are described in Tibetan books as beautiful, heroic, awe-inspiring, stern and majestic.

From Judith Simmer-Brown's, Dakini's Warm Breath: The Feminine Principle in Tibetan Buddhism (Boston & London: Shambhala Pub., 2001,) 154-156:

"The heruka (tRak-thung) is a masculine deity, wrathful or semiwrathful, who represents the dynamic of compassion and skillful means in Tibetan tantra. The heruka traces its origin to the same pre-Buddhist traditions of India as the dakini, in the retinues of wrathful Siva or Mahakala in which he served as terrifying demon.

Heruka literally means "blood-drinker," and in a tantric Buddhist setting this refers to drinking the blood of self-cherishing, doubt, and dualistic confusion.* The tantric interpretation of the term heruka derives a further meaning: his nature is beyond conventional cause and effect, existence, and duality. He is the ultimate expression of the radiantly selfless qualities of the mind. Having drunk the blood, the heruka experiences bliss. He is fearlessly at home in the charnel ground, and under his gaze it is no longer merely charnel -- it is a palace.

"The heruka is depicted with nine classical moods (Kartap gu) which gives clues about his manifestation. He is said to be charming, with dazzling ornaments; brave, posing and strutting; threatening, with rolling eyes and a wrathful grimace; laughing, a raucous "ha ha"; fierce, with laughter that mocks, "hi, hi, hum, phat"; fearsome, grinding his teeth and brandishing a weapon; compassionate; with bloodshot eyes and radiant skin; outrageous, with gaping mouth and clicking tongue; and peaceful, gently gazing at the tip of his nose.** The heruka embodies the mountain-like presence of the enlightened masculine principle in Vajrayana Buddhism, with its range of fierce, hearty, and gentle qualities."

They also mention some of the Attributes of Wrathful Deities:

Some of the attributes (symbolic implements) wielded by Dharmapalas such as Mahakala and other wrathful manifestations can include:

Sword (T. rtse-mdun, Skt. khadga) symbolizes the wisdom, knowledge or ability to cut through delusion or obstacles.

Flags, standards and banners (Skt. dhvaja) which represent the victory of Buddhist teaching over delusion.

An elephant goad or ankh (Skt. ankusa) for taming desires.

Spears (T. mdun) that fix or pin down.

Hammer (Skt. mudgara) mace or club (Skt. gada) that crush opposition.

Bow (Skt. ripa) and arrows (Skt. sara): action at a distance.

Vajra staff (Skt. vajradanda)

Trident (T. rtse-gsum, Skt. trishula) symbolizing the Three Jewels.

Lasso (Skt. pasa) that constrains negative forces.

Lastly, here is an interesting short-text on "Peaceful and Wrathful Forms" and a link to a another question-site where a being has asked about wrathful deities. You might find some answers here too. Hope this helps. This was a very good question. I didn't know about this and have now learned a lot researching the topic.

To add to the other answers here, the wrathful Buddhas are often seen as protectors. Mahākāla for instance is just another form of Avalokiteśvara. He (mahakala) is considered the tantric "watchdog", protecting those that appropriately practice Vajrayana, but is said to turn quickly on those that misuse those teachings.

Another well known wrathful diety is Vajrapani

According to the Pancavimsatisahasrika and Astasahasrika Prajnaparamita any Bodhisattva on the path to Buddhahood is eligible for Vajrapani's protection, making them invincible to any attacks "by either men or ghosts".

He is part of a trio with Manjushri and Avalokiteśvara. They represent power, wisdom, and compassion of the Buddhas.

In the bardo the first set of deities you encounter are the peaceful ones. Later you encounter the wrathful ones. If one realizes that both are projections on ones own mind, and does not fear and embraces the energy involved it is said one can reach liberation in the in-between state in this way.

The worst thing one can do is to fight or flee from them, these energies are not avoidable and are due to past karma/kamma. Just as when the "mirror" that reflects your last life might show you things that make you uncomfortable, to deny your bad deeds at this time magnifies the karma.

One important thing to note about these wrathful deities is that they are not devils, they are not like Mara. They are there for practitioners benefit and protection.

The peaceful and wrathful deities have a mantra as well called the 100 diety mantra.

Om Ah Hung Bodhi Chitta Maha Sukha Jhana Dhatu Ah Om Rulu Rulu Hung Jo Hung

To hear Tibetan pronunciation you can go here More information about it here