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I searched a lot regarding meanings of beeja mantras (esp. klim, sauhu, aim, hrim, shrim). Web gives overall meaning. e.g. 'aim' is saraswati mantra; may the goddess Saraswati bless you'; 'Hrim' is tantrik pranav and yogik hrudaya. That's it. And the same case for other beej mantras.
Request if I can get thorough explanations with scripture references for these beeja mantras.
Here are meanings of some beejamantras:
Beejamantra of Maa Kali: क्रीँ = क् + र् + ई + चन्दविन्दु. क् implies काली, र् implies Brahma,ई implies Mahamaya,चन्द्रविन्दु chandra implies Naada and bindu implies dukkhaharana. So the meaning of the mantra is: [May] Naaada and Brahmamoyi Mahamaya Kali remove my sorrows and sufferings and give me bliss. This is according to the Mantrarthaavidhana of the Varadatantra.(page 65):
"क काली ब्रह्म र प्रोक्तं महामायार्थकश्च ई। विश्वमात्रर्थको नादो विन्दुर्दुःखार्तिहारकः॥तेनैव कालिकादेवीं पूजयेद् दुःखशान्तये॥"
In the sanketatantra, we get:
ककाराद्विश्वमुत्पन्नं तेन सृष्टिस्वरूपिणी। रेफः कालाग्निरुद्रात्मा तेन संहाररूपिणी। ईकारश्च महालक्ष्मीर्लोकत्रयविभाविनी। तेनेयं पालिनी शक्तिः सामरस्यं च विन्दुना॥ (Ref : Purascharyarnava, page 724)
The above means the Devi Kali is Goddess of creation, destruction and preservation of the three worlds and one with Shiva.
According to the Todalatantra, क् means dharma, ई means artha, र् means kama and anuswara means moksha. Here the beeja is mentioned as क्रीँ. So the meaning becomes that Goddess Kali is bestower of Dharma, Artha, Kama and Moksha.(Ref: Shasramulak Bharatiya Shaktisadhana, Upendrakumar Das, Vol 1, page 466).
The beeja mantra of Sri Krishna is क्लीं.Here क् means Krishna, ल् means Aishwarya, ई means Santosha and anuswara means give bliss and remove dukkha. So the mantra means: [May] Krisna, the Lord of all wealth make me blissful and remove my sorrows.
The beeja mantra of Devi Durga is ह्रों. ह् means Shiva, र् means Prakiti, ई means Mahamaya and anuswara means remove sorrows and give bliss. So the mantra means: [May] Devi Mahamaya Durga who is the wife of Shiva remove my suffering and give me bliss. (Ref: Omkarnatha-Rachanavali, page 113).
Normally in non-yuktakshara mantras like ऐं, which is the mantra of Guru, Saraswati and Kundalini, the first letter denotes the deity and the anuswara has the meaning mentioned above.
Hope this answers your question.
UPDATE
The beeja mantra of Shiva is हौं. ह् means Shiva, औ means Sadashiva, Vindu means :Remove suffering. So the meaning is
May Lord Shiva, the Ever-Doer of Good, remve my suffering.
shiva-vAchi ha-kAras tu aukArah syAd sadAshivah/ sunyam dukkha-harArtham tu tasmAt tena shivam yajet.//(Reference: Ahnik-Kritya, Shyamacharan Kaviratna VidyAvAridhi, Vol.1, page 79).
Similarly there are meanings of other veeja mantras in the 6th patala of the VaradA-Tantra.
Mantrarthavidhan also I think would be a basic text.
