It manifests in little things. We were waiting outside the conference room last week for our manager to get the keys to unlock it. Nobody told me to, I wasn't responsible for snacks, but I picked up the trays of pastries and brought them in and put them in the right place and joked "It's my New Years resolution to squat anything I can get my arms around." I got thanked.
In startups you often have to get things done quicker than you can hire new people to do it. A lot of people have the attitude that they have a certain circle of responsibility, which is necessary and appropriate in a large organization, but in a small organization I like it that people have internalized the goals of the organization and are willing and able to pinch hit.
I think people often get this attitude working in small businesses, like a little shop that sells knick-nacks at the beach or the summer that I got re-hired at a supermarket that owed me a favor despite not really hiring at the time. I worked about 50% at the front end and the other 50% doing odd jobs directly under the store manager which meant they'd have me paint a metal line that ran around the outer wall of the store or sub for people in the deli (learn to work the meat slicer) or bakery, etc.
In a big organization you need some rigidity, but big organizations can also be seen as a collection of small organization (e.g. "employees don't leave companies, employees leave managers")
It's a pet peeve of mine when people in a startup don't have a flexible attitude.