Overview

After app installation you can spot additional element present in Jira under "Manage apps" (1) tab named "Contacts Audit Log":

It will lists actions related to Contacts Manager app. Here is an example after a new company creation:

Feature is visible only to the Jira Administrators. More about: Contacts Audit Log

To use Contacts Manager you need to add new companies. Users with project role Administrator are the one allowed to create new entries in ‘Contacts’ tab.

Upon accessing it, if there's an entry already present, added via "New contact (1) button, you should see a similar view, with list of all companies:

“Search” (2) - filter which allows searching needful contacts from the list.
“Clear” (3) - used for clearing the “Search” field.
“Export to CSV” (4) - with this option you can export list of contacts with all information to CSV file. Contacts chosen to export is based on “Search” filter, so if it is empty, all contacts will be exported.
Description (6) - contains nothing more than descriptive information in regards to company (i.e. scope of operations/services offered) placed during creation of new contact.
Next to it, "From Project" (7) informs in which project, an entry containing company's name has been created, thus giving a chance to quickly associate its operational area.
"Members" (8) presents in a numeric form how many people have been added to listed company, presenting potentially how big such entity is.
"Actions" (9) menu contains three options to choose from: "Edit" (10), Edit Members" (11) and "Delete" (12). Full description of its possibilities is described on a dedicated page.