They move the price of dealing with the effect of carbon emissions onto the producer of those emissions. A price which affects all of society but which is not considered by the producer is called a negative externality, and is exactly what we have with carbon emissions. By moving the cost of cleanup onto the producer you get a more appropriate price for whatever the thing is.
So for example consider electricity generation. A given supplier needs to buy electricity from producers: they don’t care whether that is wind or coal power. By including the price of carbon in the coal power we make it less competitive, so less coal power will be bought and less coal will be burned.
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