Telescopes are tubes designed to capture distant light, bring it to a focal point, and enable the image to be magnified. The eyepieces are of various focal lengths and provide magnification. In astronomy, the aperture of the telescope - the diameter of the lens or mirror - is of more importance than in terrestrial telescopes, because the light from distant objects is fainter. Astronomical telescopes are often referred to by their aperture size (eg 4", 130mm, etc).
Lenses and mirrors need to be of good quality, otherwise your viewing is spoilt by distorted images and false colour (aberration). All the makes listed on this site are known for their quality optics.
There are only two main types of telescope - refractor and reflector. A refractor is the original kind, the sort Galileo used, and consists of a tube with an objective lens at one end and an eyepiece (ocular) at the other. The lenses are shaped a certain way to refract light and bring different wavelengths to a focus in the eyepiece. The image in a refractor is left-to-right reversed but right way up, so it can be used as a terrestrial scope.
A reflector - which was invented by Isaac Newton - uses a mirror to collect the light. Rays reflect off a curved mirror - either spherical or parabolic in shape - at the bottom of the telescope, and return up the tube towards a focal point. Before they reach it, they are diverted by a second mirror - flat and set at an angle - and directed out to reach their focal point in the eyepiece, which is set in the side of the tube, near the top. The image is inverted, which does not matter for astronomy, but does mean that a reflector is not suitable for terrestrial viewing.
The two types of telescope look quite different, but in the beginner's range the choice between them is largely a matter of taste and size. There are other telescopes which are a combination of the two. These are called catadioptric, and use both lens and mirror to correct the distortions produced in each.
In the last decade, 'Go-to' telescopes have become very popular. They have a handset and an in-built computer programme, and at the press of a button you can go to anything in its data base. Some beginners find these very helpful when faced with a sky-full of unknown objects.
An astronomical telescope usually has a much smaller refractor telescope mounted on one side. This is a finderscope and enables you to locate the area you want before looking with increased magnification (and a reduced field of view) through the eyepiece. Some telescopes use red dot finders instead, which have no magnification; you align the dot with the object you want to observe.
The eyepieces supplied with the telescope are of different focal lengths. It is best to put the longer one in first (usually 20mm or 25mm), as this provides less magnification but enables you to see more sky. When you have centred your object, you can change to greater magnification, if desired, by using the shorter eyepiece. Another way to increase magnification is to place the Barlow lens between eyepiece and barrel. In both cases, you will then have to re-focus.