As the other answers mentioned it cause the intermediate floating point results to conform to the IEEE specification. In particular x86 processors can store intermediate results with different precision from the IEEE spec. The situation gets more complicated when the JIT optimizes a particular computation; the order the instructions could be different each time resulting in slightly different rounding.
The overhead incurred by strictfp likely to be very processor and JIT dependent. This wikipedia article on SSE2 seems to have some insight into the problem. So if the JIT can generate SSE instructions to perform a calculation it seems that strictfp will not have any overhead.
In my current project there are a few places where I use strictfp. There is a point where potential cosmic rays need to be removed from pixel values. If some outside researcher has the the same pixel value and cosmic ray in front them they should get the same resulting value as our software.