FLOPS stands for Floating Point Operations per Second, and is often used as a way to measure the speed of computing power without bothering about bottlenecks like I/O speed. Typically measured in MFLOPS (Millions of Floating Point Operations per Second).
Linux has its own system called BogoMIPS (Bogus Million Instructions per Second) which gives quite a good indication of the relative speed of fixed-point arithmetic. This is calculated for each processor core and logged at startup (typically going into /var/log/messages or /var/log/dmesg) and worked out before any real I/O is done to make sure it's fairly consistant. BogoMIPS have a couple of drawbacks, since it doesn't look at floating-point calculations and doesn't account for any oddities in your multi-core setup, so it isn't much use for comparing different processor types (Mac vs PC etc) for some applications (e.g. ray tracing or complex modelling) but it does provide a very quick-and-easy comparison with zero actual work.
However, I would be very wary of looking purely at FLOPS (or BogoMIPS) as a measure of overall system speed since they don't account for other speed problems. If your system starts paging to disk then the processor's speed doesn't actually as make much difference as extra RAM, for example, and RAM speed and motherboard (FSB) speed also play a very large role.
I'm not saying you shouldn't be looking for FLOPS measurements but you may be better off looking at overall profiling performance.
With the disclaimers out of the way, you might like to look at http://linux.maruhn.com/sec/flops.html
Hope that helps,
—Robert J Lee