You need first to finish the whole quest line of a kingdom to be able to enter the 'Explore' option of such kingdom. Explore is useful to obtain rare traitstones needed for troops traits. The traitstones obtainable through Explore are different for each kingdom, basically related to the kingdom main colors. The enemies you face when exploring are mostly random. Be careful as sometimes even high-level mythic troops may appear.
Once you have the 'Explore' option available, simply select it and win the corresponding battle to get the achievement.