The Devi Bhagavatha Purana describes the origin and importance of Rudrakshas as follows.
The origin of Rudrakshas [dark beads of Tree, termed Elaeocorpus
Ganitrus in Latin language] or Lord Siva’s tears, extensively used as
Prayer Rosaries, goes back to Maha Deva’s killing Tripurasura, who
sought to destroy the Universe and whom all the Devas, Brahma and
Vishnu failed to control. Maha Deva concentrated with His eyes wide
open for several years together to create a very highly potent weapon
by name ‘Aghora’ with which to annihilate the Demon and in the process
trickled tears which produced a stream from where sprang a Rudraksha
Tree.
The Rudraksha Seeds are of thirty eight varieties. From Lord Shiva’s
right eye, signifying ‘Surya Netra’ (Sun God), emerged from the Trees
that yielded twelve kinds of yellow colour seeds;from His left eye,
signifying ‘Soma Netra’ (Moon) came sixteen varieties of white
coloured beads, and from the Lord’s third eye on His forehead
representing ‘Agni Netra’ ( Fire) came ten varieties of black colour.
The white variety of the beads are meant for wearing by Brahmanas, the
red colour by Kshatriyas and the black coloured beads by Vaisyas and
others. ‘Eka Mukhi’ Rudrakshas represent Siva Himself the wearing of
which washes off even the worst sin of a killing a Brahmana’; two
faced one represents Deva and Devi destroying two kinds of sins among
‘Pancha Paatakas’;....
Further important informations on Rudraksha from the linked page:
1)Wearing one- faced, five- faced, eleven- faced or fourteen- faced
Rudrakshas is highly recommended.
2)Medical values of wearing Rudraksha malas (rosaries) are said to be
immense in warding off depression, stress, diabetes, cancer, heart
and blood related diseases. Close contact of body parts like head,
heart, neck, ear and hands assures protection from ill health.
3)All vedic acts are to be accompanied by wearing Rudraksha Malas like
Sacrifices, Vraths, Pujas, holy baths, Shraddhas, Solar and Lunar
Eclipses, Uttarayana and Dakshinayana ‘Samkramanas’(entry timings),
and Full Moon and New Moon days or Pournami and Pradhama days.
4)However one should not touch or consume wine, meat, tobacco, onion,
garlic and such impurities as also during mating, since these
constitute atrocious insults to Maha Deva.
5)However, Sage Narayana quoted Maha Deva telling Kartikeya that any human being irrespective of caste or even animals or other species
carrying Rudrakshas would be immune from sins as an ass carrying a
load of the beads died on way but had salvation!
&6 He who holds thirty on neck, fourty on head, six each on ears,
twelve each on hands, sixteen each on arms, one each on eyes, one on
hair or crown, and hundred and eight on breast totalling two hundred
and fifty one become Maha Deva Himself
The importance of Rudraksha is well highlighted in the following Linga Purana verse which states that Shiva does not accept Puja of those devotees who do not wear 1) The Tripundha(on forehead using Bhasma or otherwise) & 2)the Rudrakshas.
Hence, for Shiva Devotees(or generally) the importance of Rudraksha is supreme.
Vina Bhasma Tripundrena Vina Rudrakshamaalayaa ||
Pujito 'Api Mahadevo Na Syaat Tasya PhalaPradah||