The magnification of any lens is determined by its focal length. For macro photography we are also concerned with how close we can get to our subject. These two factors, focal length and minimum focusing distance, determine the lens's maximum magnification ratio, sometimes referred to as "reproduction ratio". The closer you can get to your subject with a lens of a given focal length, the higher the magnification ratio you'll achieve.
The classic definition of a macro lens is one that has a maximum magnification ratio of at least 1:1, or "1x" in lens specifications. This means that a subject can be reproduced at full size on the camera's image sensor: a 10 mm object can be projected onto the sensor as a 10 mm image when the lens is sufficiently close to the subject. A maximum magnification ratio of 1:2 or "0.5x" would mean that the maximum size that an image of the same 10 mm object could be projected onto the sensor would be 5 mm, or just half its true size.
Macro lenses are specifically designed to deliver optimum optical performance at very short focusing distances and will usually be sharpest at close range, but that doesn't mean that you can only use them for macro photography. Many macro lenses are also capable of excellent performance when shooting normal subjects at normal distances as well.
Another important characteristic of macro lenses used at short range is that they have very narrow depth of field. That means they have to be focused very carefully to get the desired details in perfect focus. A tripod can make focusing easier in some situations. You might have to stop the aperture down quite a bit to achieve sufficient depth of field with some subjects. But shallow depth of field can be an advantage, emphasizing the essential in-focus detail while defocusing and de-emphasizing distracting background.
The "minimum focusing distance" lens specification can be confusing. Minimum focusing distance is measured from the subject to the rear focal point of the lens, which is at the image sensor plane in the camera body. The term "working distance" is used to describe the distance between the subject and the front element of the lens.