Pomegranate molasses (or pomegranate syrup) is a thick, sweet, sticky syrup that's used to flavor Mediterranean and Middle Eastern cuisine. It's used as a marinade, an ingredient in sauces and dips, and a beverage sweetener. It's basically a reduction of pomegranate juice that's been boiled down with sugar and lemon juice.
Pomegranate molasses is not the same as grenadine syrup, which is a sweet pomegranate-based syrup used to flavor and add color to cocktails. Pomegranate molasses is tart and fruity, and the color is a much darker red, closer to brown.
Pomegranate molasses is commonly found in Middle Eastern markets, but can also be purchased online at various sources. You can also make your own using Alton Brown's recipe. One of my favorite things to do with pomegranate molasses is to add about a tablespoon to a small bowl that has 2 tablespoons of olive oil in it and use it as a bread dipper. The tartness of the pomegranate mixes well with the fruitiness of the olive oil. I also like to use it as a marinade or glaze for lamb, chicken, or fish - brushing them with pomegranate molasses before roasting gives them a wonderful flavor.
Pomegranate molasses is also a key ingredient in Persian dishes such as fesenjan (a Persian stew made with chicken and walnuts) and muhammara. It's also wonderful added to some plain yogurt and some mixologists have been using it as a "secret ingredient" in cocktails.