Firstly, you must understand how a meter works. All meters read/measure light ... then the meter reports this measurement as a Medium Gray (usually 18% or 16% gray).
So what does all this mean?
It means if you reflectively measure a black wall, center the needle, take a shot and make a print (making no adjustments in the processing and printing) ... you will end up with a photograph of a gray, 18% wall.
If you reflectively measure a white wall, center the needle, take a shot and make a print (making no adjustments in the processing and printing) you will end up with a photograph of a gray, 18% wall.
That is the basis for all light meters. The photographer needs to adjust the camera settings to reflect what they are capturing. In this case shooting a black wall, which is darker than 18% gray, you center the needle and then override the meter's recommendation and underexpose a few stops from the meter recommendation, (either aperture/shutter speed/ISO or a combo of those adjestments), in order to capture an exposure which is close to the actual scene and which requires minimal post manipulations. If the wall is white, the process is similar to the black wall but for white you override and overexpose from the meter's recommendation (aperture/shutter speed/ISO) in order to properly expose for the sdene.
There are two types of light meters. One is reflective and works similarily to the meter in the camera. A reflective meter measures the light bouncing/reflecting of the subject. The other is called an incident meter, it reads the light originating from the light source (see gray card). Both types meter for medium gray.
A modern digital camera light meter is a very complex, computerized device. Your camera computer takes the medium gray measurement and depending on your meter selection (Average, Matrix, Spot, et al) will manipulate the medium gray measurement (internally override the basic meter recommendation of medium gray) and attempt to optimize the meter reading to match the scene.
There is also a device called a Gray Card. It is colored to reflect medium gray. Armed with a gray card, you don't have to interpret the meter's recommendations for over/under exposing. The Gray Card is reflects how the meter measures. So, if you use a gray card you typically won't need to make any adjustments. (An incident meter and a gray card should deliver similar measurements/readings/recommendations even though the incident reading is measuring the light source and the gray card is measuring the light bouncing off the subject.
Metering is not a snap and I hope I have provided you some food for thought prompting you to grab some reading material and expand your working knowledge of photography and light and start experimenting with manual exposures.
Understanding how the meter works and making exposure adjustments reflecting your understanding of metering and light is a giant step to becoming a better photographer.