Although it was billed as a "civil war", it seems the recent violence in Lebanon was Hezbollah eliminating a bunch of rival militias before they could pose a threat to its power. According to a lot of reports, rival militia members, many of whom are simply hired guns, ran away without firing a shot. The Lebanese army didn't do anything, for fear of not being able to do anything.
Hezbollah gains a lot of its strength from its provision of social services - schools, hospitals, welfare programs, agricultural centers, etc. These gain it loyalty amongst Lebanon's Shia population, through building the credibility of the organization (compare Hezbollah's actions after the summer 2006 war to FEMA in Katrina), trust amongst members, basically social capital. That loyalty in turn is what gives Hezbollah military strength - fighters willing to die for the cause. The other militias in Lebanon do not have these broad social/political structures.
Hezbollah's social services are thus the source of its military power. New militias that attempt to join the game have to go through a period of vulnerability - it takes time to build loyalty and social capital in order to get fighters willing to die for you, and I guess Hezbollah decided to strike before its rivals crossed that threshold.
Hezbollah is being described as a "state within a state." But it's not within anything, the 'state' of Lebanon exists just like the 'state' of Iraq. Little legitimacy, little actual power. So Hezbollah is really just a state by itself.
I haven't been following the current violence in depth, but some good sources are Abu Muqawama, BBC, Ilan Goldenberg at Democracy Arsenal, the Angry Arab, and the Media Shack who has been posting on Arab media reactions to what's going on.