Hamd (حمد) is ‘praising someone because of something good he/she did’. Praising someone when that good thing was made for you is ‘shukr (شكر)’. In English, this is called ‘thanksgiving’. Praising someone because of something he or she owns without having spent effort is ‘madih (مادح)’ only; and we call it ‘praise’.
When you tell someone that he/she behaves you well, it is hamd, shukr and madih at the same time. Talking about the good thing a person did by saying, “He/She is good.” is hamd and madih, but not shukr. Saying, “He is tall and intelligent” is madih only because, he did not acquire those qualities by his effort. These are nested circles of praise, as can be seen below:
Every shukr is hamd and madih. Every hamd is madih but, may not be shukr. Not every madih is necessarily hamd or shukr.
The prefix ‘al’ at the beginning of the expression “Al-hamdu lillah” makes the word ‘hamd’ a generic noun, making the meaning: “All of hamd belongs to God.” Since the meaning of ‘hamd’ is ‘praising someone because of something good he/she did’, the meaning of “Al-hamdu lillah” becomes: “Doing everything right and well belongs to God.”
الْحَمْدُ لِلَّهِ رَبِّ الْعَالَمِينَ.
“Doing everything right and well belongs to God, the Lord of universe.” (Al-Fatiha 1:1)
. Raghib al-Isfahani, Mufradat, Art. حمد .