To many Americans and Canadians, the Rockies are synonomous with the very word "mountains". Thought of as high, majestic, craggy, and snowy mountain walls that march down the west edge of the plains uninterrupted from the Arctic to Mexico, the Rockies and their "Purple Mountain's Majesty" are an important part of every North American's mental picture of his country.
The truth is, though, that the Rockies in the United States are neither particularly high, majestic, rugged, snowy, steep, monolithic, or uniterrupted, at least compared to most other mountain ranges of similar renown. The Himalayas, Andes, Alps, Caucasus, and Alaska Range are all far more awesome when it comes to giant, jagged snow-covered summits. The most impressive section of the Rockies is the Canadian Rockies, a huge glacier-clad rampart that makes most of the U.S. Rockies seem like foothills.
The borders of the Rockies are reasonably clear. The eastern edge is where the ranges rise directly from the Great Plains, generally following I-25 in the United States. The northern edge is the Liard River, and the western edge in Canda is the great valley of the Rocky Mountain Trench. In the U.S. the western edge of the Rockies is indistinct, where the high ranges of the Rockies merge into the deserts of the Great Basin. The southern limit of what are usually called the Rockies is where the San Juan and Sangre de Cristo Ranges peter out in central New Mexico.
The Rockies are fairly high in the world scheme of things, about as high as the Alps, the Atlas Mountains of Morocco, and the Zagros Mountains of Iran and Iraq, all in the 14,000'/4500m range. However, the Rockies are far from any ocean, and rise from plains and deserts at elevations of about 4,000 to 8,000 feet, lowering considerably the local relief. The Canadian Rockies are lower than the ranges south of 49°, with only three summits over 12,000', but they are still more impressive in appearance due to more glaciation and steeper slopes.
Generally speaking, the U.S. Rockies are exceptionally gentle, rounded, easily climbed peaks, especially in light of their great height. There are precious few Rocky Mountain summits that offer the scenic grandeur and rugged craggieness of, say, the Alps--the Teton Range in Wyoming, the Crestones in Colorado, and the Sawtooths in Idaho come to mind, but little else. From a distance, especially from the expansive flatlands of the Great Plains, the Rockies look very impressive and pointy, but perhaps only twenty major summits in the entire range require any technical mountaineering skills or gear whatsoever. Mount Elbert (14,433'), the highest peak in all the Rockies, is so gentle people have ridden bicycles to its summit.
Similarly, the U.S. Rockies are not a very snowy range--there are a few small glaciers in Montana and Wyoming, and snowfields can be found on all the higher peaks at any time, but in general these are not snowcapped mountains, since from July to September virtually any peak can be climbed without having to deal with any snow.
Finally, the Rockies in the United States are not a single, uniterruppted mountain wall. Instead, they are a collection of about a hundred separate ranges spread out over six states, often with wide gaps and plains between individual ranges. The term "The Rockies" is so broad that in any local context it is virtually meaningless. Trying to make sense of all the individual ranges can be very confusing, as they are spread out over a huge area and often are completely separated from other nearby ranges, even though they are all part of the Rockies. Browsing through the range hierarchy on this site can help you figure it all out.