You probably want to look at around 20% of your daily calories from fats.
In terms of sources you fats that come from fish, nuts, olive/canola oil.
As far as good fats being good for you here are a few reasons:
1. Lower bad cholesterol and raise good cholesterol
2. Feed your brain with nutrients and improve its function
3. Reduce inflammation (This is the major benefit of how they help your heart as the more stressed, clogged and inflammed your arteries are the harder your heart has work)
4. Help with your skin
5. Improve your mood
6. ....etc
There are tons of reasons, but make sure you are taking the right kinds of fats and not the trans or saturated ones.
If you don't eat much fish, I would recommend supplementing with a fish oil. Make sure it is molecularly distilled (very important as if it's not there is a good chance there are pollutants in it) and pharmaceutical grade (this will avoid taking tons of pills in a day). The active ingredients in the fish oil you want to look for are called EPA and DHA. That is what will give you the benefits described above. Look for the EPA and DHA to be at least 300mg and 150mg per pill (more the better). The fish oil product will have the EPA and DHA quantities right on the bottle. If it doesn't don't buy it.
In terms of how much of the fish oil pills/liquid to take, I would recommend around at least 500-1000mg of EPA and 200-400mg of DHA daily. If you get the right kind of fish oil pills this would be around 2-3 pills a day. If you buy a low grade fish pill, it would be around 10 pills a day at least.