Photographers: Can you tell me what difference between a 75-300mm and 55-250mm lens for Canon?

55–250 will give you a wider angle and less telephoto. 75–300 will give you greater telephoto and less wide angle. The lower the first number, the wider the field of view. The higher the second number, the closer you can bring the image.

But, you also have to take into consideration the diaphragm opening of the of the lens to account for depth of field. http://www.mir.com.my/rb/photography/fototech/htmls/depth.html

I would get two lenses. An 18–55 and a 55–300. This will cover most of your photography needs for a beginner. If you can’t afford the two lenses, most Canon cameras have a 55mm lens that comes with the camera. Then get the 75–300. You will find, most of the time, you will not use the full 300. Some lenses become a bit soft at the 300mm range unless you use a lens like this. http://www.usa.canon.com/cusa/consumer/products/cameras/ef_lens_lineup/ef_28_300mm_f_3_5_5_6l_is_usm

You will notice the price is high because the optics are much better as compared to, http://www.usa.canon.com/cusa/consumer/products/cameras/ef_lens_lineup/ef_75_300mm_f_4_5_6_iii

Since you are a beginner, taking a couple classes in photography will go a long way in helping you enjoy the hobby much more. Or get a book like this to get you started.
http://www.amazon.com/Beginners-Photography-Guide-Chris-Gatcum/dp/1465408452/ref=sr_1_1?s=books&ie=UTF8&qid=1401375024&sr=1-1&keywords=beginners+guide+to+photography

Be sure to get a good tripod with your camera since using a telephoto lens will be more sensitive to slight camera movement without one. Also, a cable release or similar shutter control will help minimize camera movement while on the tripod.

In addition to the foregoing, in general, the longer-length lens will also be heavier and longer (obviously), so on that basis a bit more awkward to shlep around for hours at a time. (That also makes the use of a tripod more welcome, because the demands of manually supporting the lens for long stretches do become wearing.)

The 55mm lens will also be able to operate in slightly lower-light conditions than the 75mm lens, which may represent loss of a full f-stop. If you’re going to be doing a lot of ambient light photography in low-light conditions, then you’ll definitely want to have a 55mm lens at least available, even if it’s not your regular lens.

What do you like to shoot? Are you partial to landscapes? (in which case you would probably want something even wider than the 55mm) or wildlife or sports? (go with the longer lens) or do you shoot a greater variety of subjects; in which case I would go with the 55 – 250mm.

My favorite lens was a 75 – 210mm. It allowed me to take pictures of people “up close” without intruding; and I could use it just hand held without a tripod or monopod.

Another thing you need to consider is the range of the f-stop. When you want to take sharply focused pictures, your camera needs as much light as possible. So, in dimly lit areas, it’s best to choose a low f-stop number, opening the aperture to its biggest size. Lenses capable of very wide apertures, such as f/1.2 or f1/4, are best for creating extremely shallow depth of field. To accentuate this effect, it helps to be close to your subject. If you want deep depth of field then the reverse is true. Many landscape photographers use high f-stops in the range of f/16 or f/22, which helps keep objects in both the foreground and background in focus.
And remember that the image quality of many lenses tends to deteriorate as you approach the extreme ends of the f-stop range. This is especially true of zoom lenses because they’re so complex.

@CWOTUS both lenses have the same widest aperture of f/4–5.6 so both will let the same amount of light in. For a lense to be full f stop faster it would need an aperture f2.8.

Thank you all for the very helpful information about camera lenses and pointers. I think that the 55–250mm is more than adequate for me. I can see why that 28–300mm telephoto lens that @Wealthadvisor mentioned has very wide field of view as well as powerful telephoto properties (and a huge price tag).

Also thanks for helping me to try to understand the important concept of f-stop. Now I think I see why when I focus on a flower the background is out of focus.

Yes. The higher the f-stop, the deeper the depth of field. (Everything is sharp and in focus from the lens to infinity.) The lower the f-stop, the narrower the depth of field. (Only the subject is in focus and clearly defined while what is between the lens and the subject, and everything beyond the subject is out of focus.) Get a book on the basics of photography and learn the basics! You’ll be able to do a lot more artistically with your camera.