The meaning of the divine name "hariH" is explained thus by shrImadAchArya:
sahetukaM saMsAraM haratIti hariH - He, who destroys the samsAra along with its root or basis, is referred to as hari.
Also, it is said:
girau govardhanAkhye tu devaH sarveshwaro hariH |
The form of the Lord stationed on govardhana parvata is called Hari and worshiping the Lord with this name protects one from natural disasters.
Alternately, hari refers to Paramatman, who destroys the sins of those who indulge in his japa, smaraNa, dhyAna and bhakti.
Hari, also means the green-hued one:
iDopahUtaM geheShu [iDopahUtayogena] hare bhAgaM kratuShvaham |
varNashcha me harishreShThastasmAddharirahaM smR^itaH ||
The color green represents tR^ipti or satisfaction and abundance. Like viewing green calms the eyes, remembering the green-hued one with the sacred name hari grants peace and the sense of equanimity. Also, bhagavAn is described as blue in color i.e. nIlameghashyAmala varNa. His Shakti, bhagavatI rAdikA, who is ever inseparable from him, is described as having a golden yellow in complexion. The Supreme Parabrahman, which is rAdhA-kR^iShnatmaka [which is the same as shiva-shaktyAtmaka] is thus a mixture of blue and yellow, described as green hued [green color results when yellow and blue are mixed]. Thus, remembering Paramatman along with chicChakti through the name hari blesses one with peace, abundance, freedom from sins and eventually from samsAra. The name is thus specifically chosen as a part of the sacred kalisantAraNa mahAmantra.
The Tantras describe navamUrtayaH of the Lord in the ShaT chakras and the granthis. The sacred name Hari refers to the mUrti that presides over the granthis stationed above and below svAdhishThAna, maNipUraka and anAhata chakras. In shrIvidyA tantra, the granthis represent the mAyA or bhuvaneshwarI bIja and the same is represented by the sacred name hariH. The same is confirmed by bhuvaneshwarI kalpa [harishabdavAchyA].
The Lord himself explains thus:
harAmyaghaM cha smartR^INAM havirbhAgaM kratuShvaham |
varNashcha me harirveti tasmAddharirahaM smR^itaH ||
- I do the haraNa of sings or agha of those who remember me.
- I do the haraNa of the havirbhAga offered in Kratus or Yagnas
- I am green hued [hartavarNaH]
Hence I am called hariH
charmAmbaraM cha shavabhasmavilepanaM cha
bhikShATanaM cha naTanaM cha paretabhUmau |
vetAlasaMhatiparigrahatA cha shambhoH
shobhAM bibharti girije tava sAhacharyAt ||