The American Statistical Association has taken the unprecedented step of issuing guidance on the use of p-values. Its statement was prompted by concerns that misuse of p-values was driving bad science.
A p-value is “informally” defined in the statement as
…the probability under a specified statistical model that a statistical summary of the data (for example, the sample mean difference between two compared groups) would be equal to or more extreme than its observed value.
Doesn’t really help much, but you have to applaud the attempt. After all, even scientists don’t really understand p-values.