Hammd [حمد]: To praise the good attributes and it is optional. Madh [مدح]: To commend the good attributes; it is both optional and compulsory; Shokr [شكر]: To thank for His graces and favors.
Considering the difference among these three words and regarding the article {al} in front the word Alhamad [الحمد], we will realize that all praises are for that Sacred Being who is the Creator of all creatures and who is free to create. He is the beauty – creator, developer of all aspects of existence, and a guide to all objectives and inclinations. Anybody who praises some body else for his good work, is in fact indirectly praising Allah, since He is the Creator and anything good, and any proper adjective and good act is a drop of that Ocean, a reflect of that Light and a Ray from that Center.
In fact, by the use of the word Alhamdo lellah [الحمد لله] which we utter, and which is a comprehensive word we praise Allah.
The word “Alhamdo lellah” is a phrase filled whith light which is uttered by the lovers in the world, which is the first life and by the paradise dwellers, in the Hereafter, which is the second and eternal life.
Imam Sadiq (s) says: One of the mules of Imam Baqir (s), my father, was lost. He said: I will praise it if I find it. When the mule was found and Imam was satisfied, he put on his dress and staring at sky, he said الحمد لله, adding nothing to it. Then he said: this word includes all the praises. I may not add anything to it.[1]
God has taught His servants to use this expression to worship and praise Him. If this training had not been done, all the tongues would have been dumb to utter anything.
source : The land of lovers by Professor Hossein Ansariann