How important are test scores in the overall admission process?
Measures of aptitude (tests) are almost always less important than measures of achievement (grades) in college admissions. Where test scores stand in importance after grades depends on the college. Highly selective colleges rely heavily on test scores to trim very large applicant pools, but even there it's not an exact science. Students with some distinguishing excellence, or an unusual or desirable background, can be admitted to highly selective schools even with modest test scores. There are many excellent colleges which deemphasize test scores and focus on the student's high school record and extracurricular activities and achievements. There is an increasing number of colleges for which the submission of test scores is optional (for the entire list, see http://www.fairtest.org/optinit.htm). If you are thinking of applying to a test-optional school, please tell the college counselor, as this will have some impact on how the school communicates with the college(s) on your behalf.
Will high test scores compensate for low-to-middling grades?
In most cases, no. When scores are higher and grades are lower, it raises questions about the student's effort or motivation. All but the most selective colleges, though, will then look at the rest of the student's folder to discern what the student's potential for success at the college might be.
More detail information on these topics can be found in the Fulton School College Counseling Handbook.