An explanation of these can be found in the noble Questions of Dharaṇīśvara Sutra:
Furthermore, O son of good family, the Tathāgata is without physical errors that can reasonably be criticised, whether by fools or the wise. How so? The illustrious buddhas have no physical errors. When looking ahead and all around, when bending and extending as he walks, in wearing the upper, lower and outer robe, and when holding the alms bowl, he carries himself with grace during the four activities. When entering and leaving cities, towns and villages his feet do not touch the ground, but thousand-spoked wheels appear and sweet-smelling lotuses spring forth, upon which the Tathāgata steps. Any beings born as animals which happen to step in the Tathāgata’s footprint, will experience bliss for seven days, and when they die be reborn among the gods. Although the robes are not in contact with even four inches of the Tathāgata’s body, even a howling wind cannot ruffle it. The radiance of his body reaches down to the beings of the Incessant hell, filling them with bliss. Thus it is said that the Tathāgata has no physical fault.
The Tathāgata is without verbal errors that can reasonably be criticised, whether by fools or the wise. How so? Son of good family. The Tathāgata speaks timely, speaks when appropriate, speaks authentically, and acts in accordance with his words. His expressions are well formulated. His words are pleasing to all beings. What he says is not repetitive. His words are elegant in expression and meaning. Each moment of his speech is satisfying to all beings. Thus it is said that the Tathāgata is without verbal error.
The Tathāgata is without mental errors that can reasonably be criticised, whether by fools or the wise. How so? He does not stray from his equipoise but carries out all buddha-activities without needing to focus his attention on them, and sees everything with his unimpeded wisdom. Thus it is said that the Tathāgata is without mental error. And just as he is without mental faults, so he teaches sentient beings the Dharma to remove every fault. This is the fifteenth tathāgata-activity of the Tathāgata.1
This is the first unique quality of the Buddha.