What does 'intercept final' exactly mean?
You are correct. The verb intercept, as used by ATC and pilots means to track to and then turn onto a given course. In your given example, "vector to intercept the final approach course", a vector to intercept is a vector which will cross the final approach course and from which the pilot will be able to commence a turn to become established on the final approach course. To intercept the final approach course means to accomplish that turn onto the final approach course.

See this additional example from an excerpt from Section 4 of the Aeronautical Information Manual (AIM)


  5-4-3. b. 1.  
  
  (c) The pilot is not expected to turn inbound on the final approach
  course unless an approach clearance has been issued. This clearance
  will normally be issued with the final vector for interception of
  the final approach course, and the vector will be such as to enable
  the pilot to establish the aircraft on the final approach course prior
  to reaching the final approach fix.