To work it out you take the largest number focal length and divide it by the widest end so in your case it would be 55 Divided by 18 which comes out at 3.05 x zoom.
So in other words times zoom is the magnicfication from the widest focal length of the lens.
In DSLR terms we don't generally think of times zoom but in mm and whilst there are superzoom lenses (these cover a wide range so are a compromise) available because lenses are interchangeable, there is a tendancy to buy lenses for a particular type of photography i.e wide angle for landscape (10-20mm) Zoom for wildlife (70-300mm) etc as the image quality is better; i.e. less barrel destortion/pin cushioning or chromatic abbertions (google these terms for examples).
There is another complication with crop factors on APS-C cameras in the case of Canon this is 1.6 which would make your 18-55 in real terms based on a 35mm film or full frame sensor the actual equivalent of 28.8mm - 88mm, don't worry to much about this at the moment though but thought I had best mention it
In the first instance if you really do want a D-SLR to learn more about photography, then I would start with the kit lens, experiment find out what you like shooting and get the necessary lenses accordingly.
With regards to the Nikon or Canon simply try them both in a shop and see which one you prefer and see how easy you find them to use. I did that and preferred Canon primarily it felt more comfortable in my hands but others I know have chosen Nikon.
There are of course other good cameras such as Olympus, Sony and Pentax but it has to be said that Canon and Nikon currently have a better choice of lenses and accessories.
Also consider that Nikon has announced the D3200 which does look a very tasty bit of kit.
Ultimately it does come down to budget.