Most people, especially newbies, get a better feel for zoom magnification by comparing a digital lens ratio to the old 35mm standard. In this case, assuming you are using the 55-250 on something in the Digital Rebel series, the maximum zoom of 250mm compares to about 400mm on a 35mm film camera, which is considered a "long zoom" lens. Your 18-55mm kit lens has a maximum 35mm equivelent of about 90mm--perfect for portraiture, and about 1/4 the maxium magnification of the 55-250. (I'm rounding off everything here.) This is about the maxium zoom that you can hand-hold, assuming bright conditions allow a fast shutter speed and image stabilization (IS) is turned on. A tripod would typically be needed for anything longer than a digital 250mm, and anything longer than 150mm when conditions are less than optimum. So, for maxium zoom with minimal hassle, the 55-250mm IS is, in my opinion, the most effective Canon zoom for the price.
I have no idea what this means: "Because it is built for the APS-C sensor, it doesn't get the focal length benefit that comes with using EF or full frame level lenses." It is not lenses that are full frame, it's the sensor in the camera. And whether you use EF or EF-S lenses, the crop factor for non-full-frame cameras is exactly the same. On Canons, the crop factor is 1.6, meaning that a 100mm lens on a full-frame camera will be like a 160mm lens when used on a crop-sensor Canon, like the Rebel line. So you're not losing any "focal length benefit," whatever that is; your lens will perform like it's even more of a telephoto.
It's a decent first telephoto lens. It's an EF-S lens which means that it was built for the APS-C sensor used in the entry level Canon cameras. Because it is built for the APS-C sensor, it doesn't get the focal length benefit that comes with using EF or full frame level lenses. It's also a bit slower than more high end telephoto lenses, meaning that you can't open the aperture really wide (more that f4 or f5.6 depending on focal length), suck in more light and use a faster shutter speed. Therefore, you'll want to use it it bright light, use exposure compensation, or use a tripod in lower light situations. However, it's pretty light, so it's easy to carry for awhile. It remains my only telephoto lens at the moment, but I'll shortly be moving up. However, I've had it for three years and it's served me well. Good luck.