A-values help predict the conformation of cyclohexane rings.  The most stable conformation will be the one which has the substituent or substituents equatorial.  When multiple substituents are taken into consideration, the conformation where the substituent with the largest A-value is equatorial is favored.
The utility of A-values can be generalized for use outside of cyclohexane conformations.  A-values can help predict the steric effect of a substituent. In general, the larger a substituents A-value, the larger the steric effect of that substituent. A methyl group has an A-value of 1.74 while tert-butyl group has an A-value of ~5. Because the A-value of tert-butyl is higher, tert'-butyl has a larger steric effect than methyl. This difference in steric effects can be used to help predict reactivity in chemical reactions.