JASP is available for Mac OS X, version 10.12 (Sierra) and above (Which version do I have?). Apple does not support macOS 10.11 and below anymore. For these older OS’s, it is possible to download JASP 0.9.2. JASP is installed by downloading and double clicking the .dmg file, and dragging the JASP icon to the Applications folder. This places JASP in your applications folder.
It might warn you that it “is a file downloaded from the internet” and it is right, but you can just click through that and everything should work fine.