I would guess that they use water as a comparison for two reasons:
1. Almost everyone has a good grasp on how dense water is, because we all use it every day. Place a normal bottle of water in front of anyone and s/he will have an idea of how much it weighs and how heavy it is to pick up. It's easy to understand the immense weight of the sun when you imagine that
if you fill the bottle with pieces from the suns core, it would weigh about the same as 150 equally sized bottles of water.
2. The metric system is based around water, 1 ml of water weighs 1 g, that's the definition of
gram. As a direct result, 1 liter of water weighs extremely close to 1 kg. The definition of a
liter/litre is 1 dm^3. So if the suns core weighs 150 kg/dm^3, then you don't even have to do any calculations to find out that it's 150 times more than water. It's therefore both easy and natural to compare densities with water.
I'm aware that you didn't ask why they compare it to water, but I included the answer to your question as well. It's the bolded part.
Fun fact about the sun: The core of the sun is 15.6 million degrees Celsius (28.1 million degrees Fahrenheit). Imagine that you'd be able to heat up a coin to that temperature and place it on the ground. The heat would then set fire to everything within a 4 km (2.5 miles) radius.