Answer:
It can be a person -- Residents can be empowered to realize and use their abilities to build and transform the community. The stay-at-home mom or dad who organizes a playgroup. The informal neighborhood leader. The firefighter who risks his life to keep the community safe. These are all community assets.
It can be a physical structure or place -- a school, hospital, church, library, recreation center, social club. It could be a town landmark or symbol. It might also be an unused building that could house a community hospice, or a second floor room ideal for community meetings. Or it might be a public place that already belongs to the community -- a park, a wetland, or other open space.
It can be a community service that makes life better for some or all community members - public transportation, early childhood education center, community recycling facilities, cultural organization