DNA methylation is part of the curriculum for epigenetics. Most people don't hear about this too much unless they study molecules and genetics. My dad is a Professor of this and he has a lecture book on gene silencing.
He has me help with his class slides sometimes because he prefers to talk and I prefer to type! That's where I learned about epigenetics. My dad's notes say that epigenetics is the study of how genes function and change based on our DNA which is inherited from our parents. Methylation also has to do with gene silencing, where, as this article also mentioned, we carry many genes which are turned off and don't function.
I've never asked my dad about this but I think epigenetics implies that DNA methylation is also something we inherit from our parents. Our genes determine which genes are meant to be on and which are meant to be off and cause methylation according to that.
DNA methylation, along with something called histone modification, determine how our DNA, and the genes in our DNA act. I think histones are a type of protein that acts similarly to methyl groups. Just like in metyhlation, histones can attach themselves to DNA and impact how they function.
What's most interesting to me out of all of this is that everything that goes on in our body- including individual hydrocarbons that make up a methyl group- is inherited from our parents. It's so interesting!