This is a part of a passage quoted from an article:
After a routine health check up with your local doctor, if he concludes you are physically and mentally sound...
Routine's definition in its adjectival form from OALD that seems to fit the context are:
1 done or happening as a normal part of a particular job, situation or process
The fault was discovered during a routine check.
2 not unusual or different in any way
He died of a heart attack during a routine operation.
However, I am unsure of which definition is more appropriate to the context. Definition #1 seems confusing; I could understand if it states "done or happening as a normal part", but the latter part "of a particular job, situation or process" doesn't make sense to me in relates to the context, because if you're going to a check up, it's obviously not a "job", "situation" doesn't make sense neither. Maybe "process" refers to the check ups as an ongoing matter that one has to go to through out their lifetime? Otherwise, I feel definition #1 fits the best.