Place the peaches, maple syrup, and lemon juice in a sauce-pot (I use a heavy-bottomed 3-quart pot).
Mash the peaches into small pieces.
Bring to a boil, then reduce the heat and simmer, stirring occasionally, until reduced and thickened, about 30 to 35 minutes. Keep an eye on the heat and turn it down, if needed, to make sure that the jam doesn't burn on the bottom of the pan (this is especially important as you get closer to it being done). Remember that the jam will thicken a little more after it has cooled, so it is ready when it is almost as thick as you would want the finished jam to be.
Remove the pot from the heat and stir in the vanilla extract. Let the jam cool in the pot for 5 minutes.
Spoon the jam into a jar (or jars depending on what size you want to use). Place the lid on the jar and allow to cool to room temperature. Note: if you are going to freeze the jam, make sure to leave some space at the top of the jar to allow for expansion).
Refrigerate the jam for 24 hours (it will thicken up more during this time).
Keep the jam in the refrigerator for 2 to 3 weeks or freeze it for up to 1 year.