Some people using Intel Macs will see an error similar to the following:
This is an issue likely following after some changes made to Mac OS in recent releases of that OS for privacy and security reasons. If it's been more than 30 minutes since you installed VirtualBox, you'll need to first uninstall VirtualBox, remove any of its files that it leaves behind, and install it once again.
Then, follow these instructions:
Go to System Preferences / Security & Privacy
In the "General" tab, click the "Allow" button near the bottom of this window where it says 'System software from developer "Oracle America, Inc." was blocked from loading'.