The light meter that's in your camera is an reflective meter.
Reflective meters measure the light that is reflected off of the subject, and determine the exposure based on that reading.

Standalone incident meters, like the Sekonic models, instead measure the light that falls onto your subject.

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There are multiple reasons for choosing one over the other:

• Incident meters are not affected by the colour of the subject. A dark-coloured subject will fool a reflective meter. This is because all meters compare the light they meter with middle grey. A dark-coloured subject will seem like a middle-grey subject in poor light, so it will try to compensate and therefore overexpose the subject. This is also the reason why you have to "overexpose" when shooting photos of snow.

• Reflective meters can also be fooled by highly reflective, shiny objects such as metals or glass, thinking a lot more light is coming from the entire scene than is truly the case.

• Some cameras don't have light meters at all. Many fully manual cameras do not have batteries, and thus you must use an external light meter for accurate exposures (mechanical cameras from the 50s and 60s commonly had selenium cell light meters, which do not require a power source other than light, as demonstrated by Dubu's comment).

• Spot meters are reflective meters with quite a small angle that is being measured. These are generally used to measure specific (important) points in a scene, which would be hard or impossible to measure with an incident meter. This could be due to, for example, distance to the subject.

• The reflective meter in your reading gives an approximate exposure of the entire scene. The metering method could be, for example, bottom-centre weighted. This means that the meter meters the entire scene, but bases the exposure especially on the light that is coming from the bottom centre in the scene. This works usually, but what if the main subject of the scene is differently exposed to light and not in the bottom centre, but in the top right? In such a case, using an incident meter would help in getting a correct exposure.

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However, one could also use an external reflective meter, even though the camera itself already has a built in reflective meter. This is because most older cameras have only one metering method (which is often (bottom) centre weighted). When spot metering becomes a necessity, an external spot meter can be used instead.

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Note that, in order to be able to make use of an external light meter, the user must be able to manually set both the aperture and the shutter speed without the camera changing either of those (also known as the manual setting). For example, the Pentax ME lacks a shutter speed dial and thus can't be used for manual exposures, in contrary to the Pentax ME Super.

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More information

• Middle grey: https://www.sekonic.com/netherlands/whatisyourspecialty/photographer/articles/understanding-middle-gray.aspx
• Difference between incident and reflective metering, and problems with reflective metering: https://www.digitalphotomentor.com/the-difference-between-reflective-and-incident-metering-and-how-they-work/