Every Mantra has a Devata, means when we recite a Mantra, we are worshipping that Devtaa. The Mantra are normally Beej Mantra which consist of a number of Swar and Vyanjan. The role of the Vyanjan is to restrict the Dhwani of Swar . In other words, we cannot pronounce the Swar without a Vyanjan, therefore, it becomes the strength of Swar.

Normally each Beej Mantra has one Swar, which ends with the Vyanjan M (shape of Chandra Bindu). For example, say for a Swara or Vowel KA, one Vyanjan (Consonant) like MA (Chandra Bindu like M ) is always added,  hence it is pronounced as Kam. Here the sound of Chandra Bindu or M, represents the power of Panch Bhoot, although the full Beej Mantra of Panchbhoota is Hm, Ym, Rm, Lm and Vm. Then, the Beej Mantra are created with a number of Swar (Vowels) to represent different Deity, Shakti etc.

That is how it is stated in Brihat Gandharv Tantra (Chap- 5), Shreenu Devee Pravakhayambee Beejanam de - Rooptam, Mantro Uchchaaren Maatren Dev Roop Prajayate.

Now the meanings of 12 Beej Mantras are given in Varad Tantra (collection in Praan Toshinee) as follows:-
Hroom :- Shivvachee Hakarastu Aukarah Syat Sadaa Shivaaya, Shoonya Chandra Bindu) is which removes all Dukh. Therefore one should pray to Shiv. Dum :- Here D is Durgaa vachakam, U is shelter. Hence the Naad is the mother of Universe, So, it becomes Mantra for Durgaa.

To be brief, Kreem for Kalikaa, Hreem for Bhuvaneshwaree, Shreem for Mahaa Lakshmee, Aim for Saraswatee or Vaanee, Kleem for Kaam or Krishn, Hum for Shiv and Bhairav, Gam for Ganesh, Glaum also for Ganesh, Kshraun (for Brahma and Narasinh) thus Narasinh, Streem for Durga, Mahaamaayaa - Maa of the Universe, one which removes all the obstacles, difficulties, Dukh and helps in Nirvaana.

My intention for this introduction of Beej Mantra is with a purpose. This is so, because, as all planets have been assigned Mantra, in the same way, Raashi or Signs have also been assigned the Beej Mantra as follows. The introduction given above can help us to get the meaning of the Mantra for related Raashi. Thus:-

Mesh :- Aum Aim Kleem Sauh
Vrish :- Aum Hreem Kleem Shreem
Mithun :- Aum Shreem Aim Sauh
Kark : - Aum Aim Kleem Shreem
Sinh :- Aum Hreem Shreem Sauh
Kanyaa :- Aum Shreem Aim Sauh
Tulaa :- Aum Hreem Kleem Shreem
Vrishchik :- Aum Aem Kleem Sauh
Dhanu :- Aum Aem Kleem Sauh
Makar :- Aum Aem Kleem Hreem Shreem Sauh
Kumbh :- Aum Hreem Aem Kleem Shreem
Meen :- Aum Hreem Kleem Sauh

(OM has a very length definition.. in short it is the Pranav Dhwani or the Swaroop of Brahm, which commands the purity of or equality of the  Mahaabeej Mantra).

I will also like to invite attention to Shreem, which is used for all the signs except for Mesh, Vrishchik, Dhanu and Meen. This one example can help us to understand the use or non use of Shreem. While doing Praan Pratishthaa for Gems or Stones or Rudraaksh, after doing the main Mantra and Prayers one finishes the Poojaa with Nava Graha Stotra, Nava Graha Kavacham and also recites the above Mantra for each Raashi also, and lastly Kshamaa Praarthanaa.
[by Raj Bharadwaj in JR group, on July 9, 2011]