Release on an undertaking is a stricter form of release than release on an appearance notice, but typically a less strict form of release than bail. If you are released by the police on an undertaking, then you will have release conditions in addition to attending court and for identification, and those conditions will depend on the crime you are charged with. The idea is that you are released based on your legally binding promise (i.e., 'undertaking') to follow the conditions.
For example, people charged with child pornography crimes are often released on an undertaking not to have contact with any children or go to certain places where children may be present (such as playgrounds, parks, and public pools).
Similarly, people charged with uttering threats against their partner are often released on an undertaking not to contact their partner or go to their partner’s house or workplace. I have a separate FAQ on these 'no contact' conditions.