It means "belonging to Ashoka" or "related to Ashoka."
For example, you might hear the term:
* Ashokan edicts: referring to the inscriptions that Ashoka had carved on pillars and rocks throughout his empire.
* Ashokan art: describing the style of art that flourished during his reign.
The word is formed by adding the suffix "-an" to the name "Ashoka," which is a common way of forming adjectival forms in English.