Instead of using a page file – such as in Windows – what type of partition does Linux use when it does not have enough memory to hold all the data that it is processing?

Swap.

Explanation:

A swap type partition is used when there is a lot of confidential or non-confidential data or information is in the system and there is not enough memory to contain all data or information because they also required space for processing then the system user swap partition from the other partitions that required.

It is one of the necessary thing which used at that time when the space of the current partition is almost full and all the data is necessary so the system user exchange space from the other partitions when they required.