As an example I will use a footrace with a length of 10 km. 
The first contestant runs at a constant speed of 10 km/h. They will finish the race after a time of 1 hour.
The second contestant runs at a speed of 20 km/h (twice the speed of contestant one) for the first 5 km of the race. This will take them 5 km / (20 km/h) = 0.25 hours. Then they run at a speed of 5 km/h (half the speed of contestant one) for the next 5 km of the race. This will take 1 hour. They will finish the whole race in 0.25 hours + 1 hour = 1.25 hours.
In this example, the first contestant, who runs slow and steady indeed wins the race, as they arrive a quater of an hour earlier at the finishline than contestant two, so there is some merit behind the phrase.
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