用意

I can't fathom what you mean.

It was some time before I realized what he was driving at.

He had some motive in telling this story.

sinister motive

evil purpose

lofty/noble purpose

intentions behind

have dubious intentions; have suspicious aims

have commendable intentions

know sb's intention

make known one's intention; express/state one's intention; make one's intention clear

be unaware/ignorant of sb's intention

In learning, concentration is required, for every character learned is worth a thousand pieces of gold.