Japanese clans fought mostly for political power, land and influence as one regional warlord tried to gain leverage over his rivals.
There were different specifics depending on the period of time you look at Japanese history. During the Heian period, the imperial family was monopolized a single clan, the Fujiwaras. After years of fighting, alliance shifting, and court intrigue, the rival Taira clan was able to seize power until the year 1333 establising their own Shoganate. Until the beginning of the 1900’s, the Shogun was the de facto ruler of Japan, using the Emperor’s status to legitimize his power.
A clan is mostly a big group of families that work together and who share the same values.