Why does the new Cygnet installation ask to unblock apache? Isn't apache a web tool? Does that mean my reports and personal private client data are going to be sent over the internet or stored on the internet? Should I block apache?
No. Your data are private. Nothing will be sent or stored on the public internet.

The reason we are using apache is to allow some new features such as shared intra-net folders. For instance, you can now create an internal private network within your office (not shared outside on the public internet but private inside your office INTRA-net) using a single shared drive, where all the Cygnet systems in your office access all client files. This feature is extremely useful for larger offices where one client might be on a different Cygnet system on different days, and the clinician needs to easily access that client's files, past history, and current session count from any system in the office.
How to allow a program to communicate through Windows 7 Firewall.
If you are using a 3rd Party firewall software, you will need to consult the help files in that software to figure out how to allow a program to communicate through the Windows firewall. Apache should be added to the "Approved," or "Allowed" list.
For more on networking your systems skip to the end of the video on using the reports feature in Cygnet