Ganapati-Mantra

gaņānām tvā gaņapatim havāmahe kavim kavīnām upamashravastamam
jyeşhţharājam brahmaņām brahmaņaspata ā naĥ shŗņvan ūtibhiĥ sīda sādanam
--GRtsamada, Rig Veda 2.23-1
(taken from http://www.vedah.com/org2/audio_vis/selected_rv/ganapati.asp )

The explanation and meaning are based on the book Essentials of Rig Veda by Dr.R.L.Kashyap:

In Rig Veda, Gaņapati, Brhaspati, and Brahmaņaspati refer to the same deity. The word "Gaņapati" occurs only twice in Rig Veda where it is identified with the deity Brahmaņaspati. In the veda, Brahma stands for the Potent Word, 'mantra' and brahmaņaspati is, naturally, the leader of the mantras. So here Gaņapati means leader of hosts of mantras, not of Gods.

Meaning:
Among the hosts of mantras (gaņānām), we invoke (havāmahe) the Leader of the host of mantras (gaņapatim), a seer among the seers (kavim kavīnām) and of highest fame (upamashravastamam).
May the leader (or eldest-- for jyeşhţharājam), the Lord among the Mantras (brahmaņām brahmaņaspata) hear(shŗņvan) us and manifest (sādanam) in us with his protections (ūtibhiĥ).

When the mantra is recited appropriately, it enters our subtle bodies and releases the concealed forces ansd leads them upwards in manifestation.

He appears in the Tantra Yoga in the form of Gaņapati, the presiding deity over the paravAk, the speech supreme with his abode in the mUlAdhAra chakra, the subtle body of every human.

This deity is also the popular elephant headed God worshipped in puraNas , whose trunk is in the form of the sacred syllable OM. He is also called as vighneshwara or the Lord of Obstacles. Physical obstacles are caused in our tasks because of our conflicting thoughts and desires. All problems of existence are problems of harmony. Gaņapati places the appropriate mantra in the subtle body using his tusk skillfully and the power ofthe mantra removes the inharmoney, the cause of the obstacle.

His power enables us to hear the voice of divine inspiration in our hearts. He is called a Kavi of the highest fame because a 'kavi' is not a mere poet, but the originator of all actions, both in macrocosm and microcosm. when he hears us, his actions for us clearly follows.