Well, you can see in the comic from Saturday Morning Breakfast Cereal what this program is supposed to do.
Java2 version 6 or newer. You can check if you have it using this command line command (Windows: Start->run->cmd):
If you get nothing or if it's telling you that it doesn't know the command "java", you probably don't have java. If you get something, it should look like this:
java version "1.6.0_06" Java(TM) 2 Runtime Environment, Standard Edition (build 1.6.0_06-b05)
If the number is 1.6 or larger, ConceptionConnection should run.
If you don't have Java or an old version, you can download the newest one at "Download".
If everything works, you can just double-click the jar file, but sometimes a compressing software like WinZip graps this file extension.
If that happens, open the jar with javaw (Windows: right click -> Open with... -> Browse -> javaw.exe in the java install directory (also tick the "always open with"-box))
Oracle pulled a fast one on us, newest (Oracle) Java versions have horrible licencing. So either choose 1.8, the last proper version, or chose OpenJDK:
Java 1.8 via Java.com
Newest Java via adoptOpenJDK.com