Habituation: habituation is the first word that comes to my mind (but see also Desensitisation).
Habituation is a decrease in response to a stimulus after repeated presentations.
For example, the first night that you sleep in a new house, you will typically notice many noises. Over the course of a few nights you learn to progressively react less and less to the common noises as you learn that they are non-threatening and do not need to be attended to.
Information reduction: There's also some interesting research on information reduction as a learning mechanism. For example, Haider and Frensch have research that shows how individuals gradually ignore task information that is seemingly not relevant to performance. Thus, part of performance improvement is attending to task relevant information. Of course, when you arbitrarily manipulate a task to all of a sudden make what was irrelevant into relevant information, accuracy suffers. Relating this cognitive psychology finding to urban behaviour, people learn that 99.9% of the time noises can be ignored during the night, but one night the noise indicates that someone needs help; a person might ignore the noise because they've learnt that it generally can be ignored.
Bystander effect: Note that the above mechanisms are typically implicit cognitive mechanisms. There is also research on diffusion of responsibility that links in more to social psychology. This has been used to explain some people's failure to help in urban settings.
- Haider, H., & Frensch, P. A. (1996). The role of information reduction in skill acquisition. Cognitive Psychology, 30(3), 304-337.