Methylenetetrahydrofolate reductase (MTHFR) is an enzyme that converts folate to it's active form, methyl folate (5-MTHF). There are a couple of surprisingly common (in the ballpark of 30-50% of the population) polymorphisms that reduce it's function. What that means is that a significant number of people can not efficiently use the folic acid found in supplements and enriched foods. Hence, they are likely to have trouble generating methyl groups and/or recycling BH4. What that translates into depends on a lot of other factors.
The two common polymorphisms are C677T (677C->T) and A1298C (1298A->C). The first means you have trouble converting *to* active folate, while the second means you have trouble *using* the active folate to recycle BH4. I'm going to label each of these as 'slow.' Everyone has two copies of the MTHFR gene, one from each parent. It's possible to have any combination of the polymorphisms, or none at all. What's not clear is how you respond to different combos. Having two slow copies means you need active folate instead of folic acid, and lots of it - on the order of twice the RDA (so 800mcg) and possibly more to make up for deficiencies.
If you have two slow copies, especially if you have a copy of C677T, then you're more likely to have a block in the methyl cycle, so low methyl groups as well as high homocysteine. If you have A1298C, then you're likely to have low BH4.
Large doses of folic acid are sometimes used to bypass the issue, and this can effectively raise levels of methyl folate in the body. The problem arises when your body goes to *use* the methyl folate and finds a ton of the wrong form of folate (because it can't be converted fast enough). It's likely to grab the wrong form by mistake, and then isn't able to use it.
Folinic acid is often marketed as active folate, and it *is* active folate, and a form found in foods. However, for those of us with two slow MTHFR genes, it does not bypass the step we need extra help with. There are a handful of supplements by Thorne and Metagenics that contain both methyl folate and folinic acid.
Salicylates can inhibit the methyl cycle, and so aspirin (concentrated salicylates) is sometimes suggested as a means of lowering homocysteine. While this may reduce the problems associated with high homocysteine, it also lowers your methyl groups, and so may just be transferring the problem elsewhere.
If you just have one slow copy, there doesn't appear to be much impairment, but I'm always going to advocate getting nutrients as they occur naturally in food, rather than forms that are only found in synthetic supplements.
Reasons to Suspect
History of stroke
Low methyl groups