We get our DNA from our Mum and our Dad, and (very simply speaking) you got 1 mthfr gene from your Mum and 1 from your Dad.
A gene is made from a long string of DNA which might look something like this:
atgcaattga. This is called the wild type.
DNA mutates (changes) very frequently. So, over the course of time the string above could change to
tgcaattgc (I've change the last "a" to a "c"). This is called the variant and the location of that change is called a polymorphism.
The vast majority of these changes have no impact at all.
Homo = the same
Hetero = different
Someone who is homozygous for the mthfr gene polymorphism got the variant copy from both their Mum and their Dad i.e. the gene (long string of DNA) with the "c" at the end. Both copies of the gene have the polymorphism i.e. homozygous.
If you got atgcaattga from one parent and tgcaattgc from the other parent the site which is polymorphic is different = heterozygous.
I just looked up the gene and it makes the MTHFR protein which helps your body process folate.
The important part is that the letter states that there is growing evidence that test for this polymorphism has limited clinical use.
And in typing all that out and then looking on the web I see this website which explains it really well!