The term "obtuse margin" refers to the superolateral border of the anterior surface of the heart. It is also known by its Latin name [margo obtusus].
The name of this border or margin of the heart is quite descriptive. If you observe the accompanying image, the angle formed between the anterior or sternocostal surface of the heart with the left lateral or left pulmonary surface of the heart, you can see that the angle between these two surfaces is more than 90 degrees, therefore an "obtuse" angle. The corresponding border between these two surfaces has to be called the "obtuse margin"!
In relation to the obtuse margin of the heart we can usually find the first branch that arises from the circumflex artery. This artery is called Obtuse Marginal 1 or OM1.
Click on the image for a larger depiction. Here is a link to an article on the "acute margin" of the heart.