As has been said, the little blinking red light comes on to tell you to upshift. But you don't always have to shift at that point; it just blinks when the car hits redline. There are usually another 500-1000 rpm available before the rev limiter kicks in.
Most cars will tolerate being overrevved a little, so sometimes it is to your advantage to ignore that light if you can stretch a straight for another second or two and skip an extra upshift/downshift. The S2000 among others can go way past its redline and is still making power up there; however cars like the SLK and the TT a serious about redline and the rev limiter will kill the fun very soon after the shift light blinks.
Also as has been said, the red number is the suggested gear for the upcoming turn. It's not always correct but it's usually in the ballpark; you'll have to use your own judgement.
The number doesn't blink to tell you you're going too fast. It starts blinking at the suggested braking/downshift point for the upcoming turn.