From PsyHelp
Pets with a strong sense of courage, strength, stamina, and ability to dodge will find themselves taking on self-made quests to rid the area of monsters. Adventuring pets can bring home anything from worthless junk (such as Figurine 7s (which are only useful if you are building an apiary add on)) to great items (such as Ornate Vases) at all levels, but higher leveled monsters tend to not drop completely useless crap. Adventuring pets in their low levels tend to gain EXP in a rather bizarre manner, usually receiving more than other pets, though this quickly evens out around levels 3 and 4.
Since they require a high strength to defeat monsters, adventurous pets often do well in brawls, but only if they have good dodge, stamina, and dexterity stats. They are often good at capturing other pets in Capture the Flag games and they tend to be rather fast.