Meaning of Ganesha Shloka - Agajanana Padmarkam

Agajaanana Padmaarkam 

Gajaananam Aharnisham

Aneka Dam Tam Bhaktaanam 

Eka Dantam Upasmahe

 Pronounciation:

agajānana padmārkam gajānanam aharniśam
anēka dam tam bhaktānām ēkadantam upāsmahē

 अगजानन पद्मार्कम् गजाननम् अहर्निशम्
अनेक दम् तम् भक्तानाम् एकदन्तम् उपास्महे

Word to word meaning:
*Agaja = Parvati;  Aanana = face; Padma = lotus flower; Arkam = sun; Gaja = elephant; Aananam = face/faced; AhaH = day; Nisham = night; Aharnisham = day & night (all the time or round the clock); Aneka = more than one / multiple; #Dam = giver; Tam = you/your; Bhaktaanaam = to the devotees; Eka = single or one; Dantam = tooth (tusk since it is an elephant); Upasmahe = I meditate upon;

Meaning:  Seeing the elephant-faced Ganesha all the time, Goddess Parvati's face lighted up, just like how a lotus opens up seeing the sun and I meditate upon the Lord with single tusk, the giver of many boons to the devotees.

*The meaning of the word agaja is derived as follows: In Sanskrit, 'ga' refers to anything that moves; ga means gamana. When you add 'a' ( a negative sound) in front of 'ga' it gives an opposite meaning. So aga means something which can not move, in this context mountain or parvatam. [similarly, satya - asatya; dharma - adharma etc.]. The letter 'ja' means to be born out of / from; Thus, agaja means born from the mountain or the child of the mountain, in this context, Goddess Paarvati who is the daughter (suta or tanaya) of the parvata raja or himavanta (hence himaja) or giri (hence girija). 

#While reciting this shloka many people make a common mistake saying "aneka damatam bhaktaanaam", it is actually two sounds or words "dam tam" which should be pronounced with a very brief pause between the sounds.  Because, if you say it as 'damtam' as one word, it sounds like 'dantam' which means tooth, and thus 'aneka danatam' gives the meaning of teeth, which is not true. We all know that Lord Ganesh has only one tusk (tooth). So it should be "aneka dam tam bhaktaanaam".