Cost index is a made up figure, which when input into the FMC is used to calculate ECON speed. The higher the cost index number, the faster the aircraft flies. Basically, the company decides on the cost of keeping the aircraft in the air, and includes all sorts of costs such as crew, aircraft operating costs, fuel etc.. They then decide whether they want the aircraft to fly faster or slower and adjust the cost index as needed.
For example, on the 744s at Cathay, we normally use CI-80. On certain flights, where the connection time is tight in Hong Kong for passengers, they might flight plan a CI or 250, or 500. This makes the aircraft fly faster. On the other end of the scale, CX255 leaves HKG at 00:45ish, and cannot arrive before 6am due to curfews at Heathror. a CI-0 is used to make the aircraft fly slower. Beyond around 500-600, it does not make a difference what you input, because the aircraft cannot fly faster, and will obviously not deliberately overspeed the aircraft, but a figure up to 9999 will be accepted by the FMC.
The airline cannot tell an aircraft to fly a certain high or low speed, because that speed will always be different at different altitudes etc.. By giving the FMC a CI, it works out the best fast or slow speed to fly based on the conditions at the time.
It's a little hard to understand, and hopefully I have not confused you too much!!