What is the meaning of: "describing the Benefactor with elective beauty, whether by the recipient of the bounty or by others"?

The phrase "Worship with beautiful choice" is the linguistic definition of praise (hamd). Its meaning is to describe the praised one with His beautiful attributes that He possesses by His own choice, with the condition of glorification. The phrase "from the one who is blessed or another" means that praise does not depend on the existence of benevolence from the praised one to the praiser, which makes it more general than gratitude (shukr).