It’s best to keep the contact information of your nearest recruiting office or your actual recruiter; they are your best bet for getting your scores. ASVAB scores are valid for up to two years before you need to retest so most offices will send your current scores via mail. If you can’t get yours by mail, you can pick them up from your local recruiting office.
Candidates taking the ASVAB are given a AFQT (Armed Forces Qualifying Test) score which is simply a combination of your scores from four tests (Arithmetic Reasoning, Mathematics Knowledge, Word Knowledge, and Paragraph Comprehension). This AFQT score is represented as a percentile (from 1-99) which depicts how well you scored compared to other test takers. For example, if your score is a 57, this means that you scored better than 57% of the other test takers. The AFQT score is used to determine whether you are qualified to enlist in the U.S. Armed Forces.
To enlist in the United States armed forces, you must take an entrance examination called the Armed Services Vocational Aptitude Battery (ASVAB). The ASVAB test helps the military determine your qualifications for enlistment. The ASVAB first appeared in 1968. By 1976 it was required by all branches of the military. The test was completely redone in 2002.

A good score on the ASVAB is different than a minimum required score.  Each of the military branches will have their own minimum required scores (see below).  In practice, however, each branch will be more selective in their recruiting.  A score of 50 on the ASVAB implies that you scored as well or better than 50% of comparable test-takers.  Since ASVAB scores are used for many purposes (e.g., enlistment eligibility, military job placements, and career exploration), it is important that you score well on the ASVAB.  A score of 60 or better should be your minimum target.
The questions that have a tendency to arise rather quickly are something along the lines of “why is this test so important?” and “What is the overall purpose of this test?” Well, first it is important to define the actual test and to assess the colorful history of the test. The Armed Services Vocational Aptitude Battery test (ASVAB) is a test that was officially formatted in 1968 with the intention of mentally preparing soldiers with knowledge that identifies with the following: