You link to existing records by using the "Extend" functionality of the Import feature.  This creates the relevant links and Related Item records.

Here's a worked example with a basic 1 line CSV file:

The "Case" column is important.  It contains the Case number, which is also the Object Reference, and will be used to "lookup" / link to the activity to CASE-3243:

1) Save the file as a CSV and create a new import job.  Start > Import > Activities - Tasks > Select the CSV file > Next > Next again > Map the Activity fields > Extend - Related Case:

2) Click Case in the Field section > Set File Field to Case > Set Matching Field to Object Reference (this is the mapping that ensures the records are linked and related item records are created):

3) Run the import.  It will import the record(s) and create the related item Activity Link record(s):

4) Approve the import if you're happy with the Import Job results (displayed on the Summary and various other tabs of the import).

5) The records will be correctly linked.  A new Activity has been created and it has been linked to the existing Case: