What are the micro and macro averages of precision and recall?

The micro average is calculated by summing up the individual true positives, false positives etc across the classes and then calculating precision and recall based on these numbers.

The macro average is calculated by finding the precision and recall for each class and then averaging these.

Macro average gives an idea of how the model performs across all classes (e.g. even classes with very little data), whereas the micro average takes into account the amount of data in each class.

More info here.