Al-hamdulillahi rabb al-alamin
All praise is due to Allah, Sustainer of all the worlds
The following are excerpts of commentary on this ayah, based on Tafsir Ibn Kathir and other sources:
The meaning of hamd is praise and extolling. It also carries the meaning of ridaa, or pleasure and is the opposite of dhamm, or blame. Its meaning is more general and inclusive than that of shukr, or giving thanks, because it encompasses this as well as giving the meaning of praise. Similarly shukr is only expressed as a response to a favour whereas hamd is expressed both as a response to a favour as well as a spontaneous action of dhikr. It is in this respect that ibn Abbaas (RA) said, "al-Hamdulillaah is the statement of every thankful [servant]."
Therefore by saying al-Hamdulillaah, the servant is praising and thanking Allaah Alone due to His greatness, unity, perfection, His Beautiful Names and Attributes and His innumerable favours and blessings that none can encompass save He. It is indeed an amazing statement that encompasses something that volumes would be unable to express and created intellects unable to enumerate! All praise belongs to Allaah!