That is saying that for every Watt that the heatsink tries to dissipate, it will heat up by 12 degrees Celsius. Hence, 12 degrees C per Watt. So, knowing this, obviously a lower number is better.
Remember, this number does not include the resistance of the thermal grease material that sits between the heatsink and the component, and the component case itself also has another thermal resistance between the case the die/junction case which is actually generating the heat. That means that the more thermal resistance you have between the heatsink and the die/junction (or whatever is actually generating the heat), then the temperature of the the die/junction becomes higher and higher above the heatsink temperature.
Example 1:
-a heatsink with 10C/W
-0C/W between the heatsink and junction/die
-junction/die dissipates 3W
Then the heatsink will increase to 10C/W * 3W = 30C above ambient temperature. Since there is 0C/W between heatsink and junction, then their temperatures are the same so the junction temperature is also 30C above ambient. This is the ideal case and never happens in real life.
Example 2:-a heatsink with 10C/W
-3C/W between the heatsink and junction/die
-junction/die dissipates 3W
Then the heatsink will increase to 10C/W * 3W = 30C above ambient temperature. But, now we have 3C/W between the heatsink and the junction. This means that the junction will be at a higher temperature than the heatsink. The junction temperature will be (10C/W+3C/W)*3W = 39C rise above ambient temperature.