hrdaya means heart
hṛ da ya

This is the mantra from the Prajñāpāramita Hridaya Sūtra or Heart Sūtra. Prajñāpāramita the bodhisattva has another mantra. To see the whole Heart Sutra in siddham script look here.

Traditionally thought to be a Sanskrit text, it now seems almost certain that the Heart Sūtra was composed in China around the 7th century, although it incorporates verses from the Chinese version of the Large Prajñāpāramita texts. It is entirely possible that Xuanzang back translated it into Sanskrit during his trip to India. The evidence for this conclusion are presented in an article by Jan Nattier: The Heart Sūtra : a Chinese apocryphal text? Journal of the International Association of Buddhist Sudies. 1992 Vol. 15 (2), p.153-223. I have a precis of this article on my blog.

Mantra

Siddhaṃ

The Heart Sutra Mantra

Tibetan - Uchen

The Heart Sutra Mantra

Transliteration

ga te ga te pā ra ga te pā ra saṃ ga te bo dhi svā hā

gate gate pāragate pārasaṃgate bodhi svāhā

Notes on the Heart Sutra Mantra

Conze's translation reads: "gone, gone, gone beyond, gone altogether beyond, oh what an awakening, All hail!"

The words of the mantra are in the feminine vocative case. The vocative case indicates that someone is being addressed. so that gate means not simply 'gone', as it is usually translated, but "O she who is/has gone!". It is common-place for Buddhist dhāraṇī to use this device. Later tradition interprets it as addressing Prajñāpāramita (ie Wisdom, considered feminine in India), however this overlooks the very widespread use of the the feminine vocative in other contexts. It is also possible to take the -e ending as a masculine locative, but most scholars seem to accept that the fem. voc. is intended. Kern, in his 1884 translation of the Sadharmapuṇdarika Sūtra, related the use of the fem. voc. in dhāraṇī to the worship of Durga.

The Heart Sutra itself describes the mantra as "Mahāmantro, mahā-vidyaa mantro, ‘nuttara mantro samasama-mantra.h" which Conze translates as "The great mantra, the mantra of great knowledge, the utmost mantra, the unequalled mantra, the allayer of all suffering". These are traditional epithets for the Buddha, so the mantra is being likened to, or equated with, the Buddha.

There are many commentaries to the Heart Sutra which attempt explanations of the mantra. Seven are recorded in the Tibetan canon. However as Alex Wayman notes:

"One feature of these commentaries [in Tibetan] on the Heart Sutra struck me quite forcibly: each commentary seemed so different to the others, and yet they all seemed to show in greater or lesser degree the influence of the Mādhyamika school of Buddhist philosophy. The writers seemed to be experiencing some difficulty in exposition, as though they were not writing through having inherited a tradition about the scripture going back to its original composition, but rather were simply applying their particular learning in Buddhism to the terminology of the sutra". - Wayman. Secret of the Heart Sutra p.136

and, having surveyed the Indian commentaries preserved in the Tibetan Canon, as well as some of the later Tibetan commentaries, Donald Lopez concludes:

"The question still remains of the exact function of the mantra within the sutra, because the sutra provides no such explanation and the sadhanas make only perfunctory references to the mantra". Lopez. The heart sutra explained. p.120.

A tradition which seems to originate with Atiśa (982-1054) relates the parts of the mantra to the stages of the path as set out in the Abhisamayalamkara (attributed to Maitreya):

gate Path of merit / accumulation
gate Path of preparation
paragate Path of insight (1st Bodhisattva bhumi)
parasamgate Path of meditation (2nd to 10th Bodhisattva bhumis)
bodhi Buddhahood

(Thanks to Ben for pointing this out to me)