This is just the warning message and if you read the sentense in full, it says miniBB runs perfectly with any earlier PHP version, beginning from 4.1.0. 4.4.7 is suitable. Recommended version is 5.x (5.2.3 at this date).
Since PHP developers are also taking care about security as we do, and implementing new functions, improving the PHP core etc. - our recommendation, as always, is just to have up-to-date software installed.
Don't forget that using open source you have a higher level of risk using the program. Offering such disclaimer via installation, we just pay your attention on the possible weak points your system might have.
That still means you can continue to execute the program.