Poblano peppers (pronounced "po-BLAH-no") are a mild variety of chile pepper used in Mexican and Southwestern cooking, perhaps most notably in the classic chile relleno in which the roasted pepper is stuffed with cheese, then coated in egg and fried.
Poblano peppers are so named because they are said to originate from the state of Puebla in central Mexico. They have thick, dark-green skin and a wide base which tapers to a point, and they're mild to medium-hot, registering between 1,000 and 2,000 Scoville heat units on the Scoville Scale.
When dried, the poblano pepper is called the ancho chili. They're sometimes dried and smoked as well.
A point of clarification: The word chipotle refers to jalapeño peppers that have been dried and smoked. Sometimes you'll see dried poblanos called anchos, and smoked ones called chipotles. But the word ancho refers to dried poblanos, whether smoked or not, and chipotle always means dried and smoked jalapeños.
Poblano peppers are good candidates for roasting. Roasting brings out the fruitier flavors of the pepper and eases in removing the skin, which can be tough and difficult to digest for some people.
Poblano peppers are sometimes called pasilla peppers, but pasillas are shaped slightly differently: longer and narrower (note that the word ancho means "wide" or "broad" in Spanish), although they do have a similar flavor profile.
When it comes to chile relleno, far too often the dish is overreliant upon the coating and stuffing, and the flavor of the chile ends up lost, to say nothing of the chile itself; rather than retaining its shape and crispness, the chile seems to vanish in a soggy marsh of cheese and sauce.
Some of this results from roasting the pepper, which brings out additional flavors but also softens it. But more often than not, the cause is that the peppers being used are not fresh poblanos but instead canned chiles of indeterminate designation.
The result of this culinary malpractice is that a great many chiles rellenos suffer from an affliction, similar to that of risotto. Due to the constraints of the ingredient or preparation time, what you get when you order it in a restaurant is almost always inferior to what you would get if it were made at home by someone who knows what they're doing.
As a rule of thumb, a chile relleno should retain its shape and be visually recognizable as a chile. If it's swimming in cheese and sauce and looks like it could as easily be an enchilada, you might want to give it a pass.
So poblanos are excellent peppers to serve with a filling. If you're preparing poblano peppers at home, you should bear in mind that there's no law requiring you to fill them with cheese. You could instead fill them with rice and shredded pork or ground beef—a stuffed pepper, basically–but using poblanos instead of the usual bell peppers.
Nor do you have to bake them like a casserole. You can stuff your poblanos and then cook them on the grill or under the broiler. Again, it's always nice for your main ingredient to be visible, rather than smothered.