PROFUSE comes from the Latin word that is close in meaning to the English word pour. So this can be related to the fact when we have excess of a liquid in a container we pour it out. This would lead to profuse being related to an excess of something, a large amount.
It is as simple as that!
Meaning of Profuse:
1. spending or giving freely and in large amount, often to excess; extravagant offer
2. made or done freely and abundantly
3. abundant; in great amount.
Sentence Examples for Profuse:
1. The ancient writers have been very profuse in their praises of this celebrated prince.
2. It looks over a green belt of profuse tropical vegetation intersected by asolitary railway line.