The RHS Award of Garden Merit (AGM) was introduced in the 1920s, and is awarded to the best plants for gardens in a range of categories. It is therefore a good starting point if you want a particular type of plant but are not sure what to choose. The award is given after trials at the various RHS locations, and may also be removed if a better cultivar appears. As an example, the crab-apple Golden Hornet was recently superceded by Comtesse de Paris, which has similar blossom and fruit characteristics but a better growing habit.
Varieties may also lose their AGM status if the RHS feels they are no longer widely available from nurseries and garden centres. Of course if you can find them from a specialist supplier (such as ourselves!) these varieties can still be a good choice.
Although the RHS AGM is a good indicator of overall plant quality, it is best not to rely on it exclusively. For example, it favours mainstream varieties that are widely available, and with good disease resistance. These are useful qualities of course, but relying on the AGM as a guide might mean you miss out on rarer plants, or plants that are perhaps a bit more difficult to grow but have other excellent qualities.
The RHS Award of Merit (AM) is a related award, first introduced in the 1880s, and focusses on plants intended for exhibition. The AGM is therefore the more relevant award for most gardeners.