advancing to graduate school; continuing to graduate studies
Refers to the act of entering a graduate program (master's or doctoral) after completing an undergraduate degree. Often used in educational contexts.
He hopes to go on to graduate school.
As preparation for graduate school, I wrote a research proposal.
大学院 is the graduate school itself, while 大学院進学 is the act of entering it.
進学 is a general term for advancing to a higher level of education; 大学院進学 specifies graduate school.
Compound of 大学院 (graduate school) and 進学 (advancing to a higher school).