Why do people behave better when observed? Why does it seem that people behave like they are supposed to when they are being observed?

For example. If you place a fake security camera on an employee, they would behave better (or at least appear to).

Alternatively, when a system or workflow becomes transparent, it seems to me that people would make an extra effort to do better since they are more exposed.

Is there any particular identified effect, cognitive bias, or phenomenon that describes the reasons behind this change of behavior?
It sounds like rational behaviour (i.e., it is not a cognitive bias). Monitoring generally creates a closer link between behaviour and social consequences (either rewards or punishments).

A huge number of theories capture ideas about how the social context influences behaviour (e.g., social norms).

In the work context, you could look at ideas around maximal and typical performance. 

That said, there is literature that looks at the pros and cons of monitoring on workplace performance. In particular, excessively fine grained monitoring can lead to increased stress, lower job satisfaction, turnover, etc. See for example Kinnie et al for a discussion.

References

Kinnie, N., Hutchinson, S., &amp; Purcell, J. (2000). 'Fun and surveillance': the paradox of high commitment management in call centres. International Journal of Human Resource Management, 11(5), 967-985.