Rational basis review refers to the review process carried out by courts when evaluating a statute. During a rational basis review, the court evaluates whether or not a statute is directly related to a legitimate government interest. This is opposed to a statute that does not appear to be connected to relevant government interests.
Rational basis reviews are a security measure to make sure that all laws and statutes are fair and constitutional. If they are not, then they may be overturned.
For example, if the government made a law that everyone must wear polka dots on Fridays, then this would likely be overturned following a rational basis review. This would be because such a law would not be connected to any government interests in any rational or reasonable way.