The magnification of a magnifying glass depends entirely on where it is placed between the user's eye and the object in focus, and the total distance between them. The magnifying power is equivalent to angular magnification. The magnifying power is the ratio of the sizes of the images formed on the user's retina with and without the lens. In the case of without lens, it is generally assumed that the user would bring the object as close to the eye as possible without it becoming blurry. This point is known as the near point, and it varies with age. A young child can have a near point as close as 5 cm, while an elderly individual may be as far as one or two meters. Magnifying glasses are typically characterized using a "standard" value of 0.25 m.
The highest magnifying power is obtained by holding the lens very close to the eye and moving the eye and the lens together to obtain the sharpest image. The object will often be close to the lens. Magnifying glasses are not always used this way. Some people find it much more comfortable to put the magnifying glass close to the object (one focal length away). The eye can then be a larger distance away, and a focused image can be obtained quite easily; the focus is not very sensitive to the eye's exact position.
A typical magnifier might have a focal length of 25 cm, corresponding to an optical power of 4 dioptres. Such a magnifier would be sold as a "2X" magnifying glass. In reality, an observer with "typical" eyes would obtain a magnifying power between 1 and 2, depending on where the lens is held.
Using this principle, a magnifying glass can then be used to focus light, specifically to concentrate the sun's beam to create a hot spot at the focus. Check this video out on YouTube.