You can copy the value form some source field to some destination field. Be aware that source and destination field must both have the same data type. For example you can copy a checkbox custom field to another checkbox custom field, but you cannot copy a text custom field to a checkbox custom field.
If the destination field is some kind of a text field (for example Summary, Description, Environment, Free Text Field, ...) it often also works even the source field has a different data type. But you should test this first.
Overwrite / Append / Prepend
For text fields and some field that can take multiple values (like checkboxes) you can choose to overwrite, append or prepend the new value to any existing value. In the case of text field, you can also choose a separator that will be put between the values (not shown in the screen shot above).
Create version if necessary
Imagine your origin issue has a version, that you want to copy to the linked issue.
If the destination field is 'Fix Version/s', 'Affects Version/s' or some custom field of type 'Version Picker', you can choose that a new version will be created in the target project, if does not yet exist. If you don't choose this option and that version does not yet exist, the user will get an error message and the transition won't complete.
However be aware, that the version will be created, even the user does not has the 'Administer Projects' permission. (Normally a user needs that permission to be able to create a new version.)