What is "One should give rise to a mind without abiding anywhere"?

Original text:是故须菩提。诸菩萨摩诃萨。应如是生清净心。不应住色生心。不应住声香味触法生心。应无所住而生其心。

The Buddha said to Subhūti: Therefore, all bodhisattva-mahāsattvas should give rise to a pure mind in this way. They should not give rise to the mind by dwelling on form; they should not give rise to the mind by dwelling on sound, smell, taste, touch, or dharmas. They should give rise to their mind without dwelling anywhere.

This passage is a summary of the preceding ten chapters, telling all bodhisattva-mahāsattvas how to give rise to a pure mind. They should give rise to the pure mind as previously described. What was said before? It was said that one should practice the pāramitās by emptying all dharma-marks: empty the mark of giving and cultivating merit, empty the marks of self, person, sentient being, and life span, empty the mark of the Tathāgata's physical form, empty the marks of dharmas and non-dharmas, empty the mark of the Buddha's dharma, empty the mark of the Tathāgata's preaching of the dharma, empty the mark of giving rise to bodhicitta, empty the mark of the stages of realization, empty the mark of attaining bodhi, empty the mark of obtaining the dharma, empty the mark of adorning the buddha-land, and so on.

After emptying these marks, the mind attains nothing and seeks nothing. One does not give rise to various mental activities dwelling on the mark of form, does not give rise to various mental activities dwelling on the mark of sound, does not give rise to various mental activities dwelling on the mark of smell, does not give rise to various mental activities dwelling on the mark of taste, does not give rise to various mental activities dwelling on the mark of touch, and does not give rise to various mental activities dwelling on the mark of dharmas. In short, one should not give rise to various mental activities dwelling on the realm-marks of the six sense objects. Not dwelling on the marks of the six sense objects means dwelling nowhere; dwelling on the marks of the six sense objects means there is a dwelling place. Having a dwelling place is non-abiding — it is not true abiding, and the mind is not pure, without the arising of great wisdom. Because the marks of the six sense objects are in fact not marks; they are called the six sense objects, but in reality they are empty. How can one dwell on what is empty? Being unable to dwell is non-abiding; even dwelling is empty. Therefore, one should give rise to bodhicitta and practice the bodhisattva's conduct without dwelling on form, sound, smell, taste, touch, or dharmas; one should give rise to bodhicitta and practice the bodhisattva's conduct without dwelling anywhere.

Specifically, how does one practice the Path without dwelling on form, sound, smell, taste, touch, or dharmas? One must clearly understand form, sound, smell, taste, touch, and dharmas: which dharmas belong to material form, which dharmas belong to sound, smell, taste, touch, and dharmas, what dharmas are included among the realms of the six sense objects, which dharmas one is particularly attached to and craving for, what mental intentions one holds when giving and cultivating merit, what one seeks, on what basis one makes one's choices, and what one's aims and aspirations are when giving rise to bodhicitta and practicing the dharma — whether one is craving certain worldly dharmas. One must deeply observe one's own mind and dig deep into one's mental intentions; only then can one master one's own mind and purify one's thoughts, be without desire and without seeking, so that one's conduct is pure and correct, gradually resonating with emptiness and gradually resonating with tranquility, thereby swiftly realizing the nirvāṇa of both the Greater and Lesser Vehicles.