Can I use Open Office on my new MacBook Air?
You have just seen GateKeeper in action.

If you are confident you downloaded a safe copy of the program, you can tell your Mac to "trust" that program and let it past the gate.


Right click on the icon
Select Open
Read the dialog and agree or disagree to let that program run


The linked article above goes into much detail on GateKeeper and I would scan it and review the steps above. If you find a lot of software you need triggers the warning, you could relax the settings, but I prefer to keep them at the defaults as I like to know when new code runs on my Mac.