That is a split power supply and it can be used in a variety of ways. They are intended to be used with operational amplifier circuits that need both positive and negative voltages with respect to ground.

However, you can use it as a single 24 volt power supply, by calling the -12 volt output ground and the +12 terminal "24". Or, use either half as a single 12 volt power supply, with positive or negative output as you prefer.

Eddiie:
The device I am connecting to requires both +12 and +24, the same thing that is stamped on the outside of the power supply.

So I guess I am safe.

I know it's taboo in forums to actually give useful information but it would be helpful if you say what the "The Device" is.

Your power supply can supply both 12V and 24V at the same time but it's weird that a "device" needs two power supplies. If it's an audio "device" you might get a hum if the two supplies are linked together.

Voltage is measured with respect to some reference point. This is why it's also known as a potential difference - the difference in voltage between two points.

You have an output that is

-12V ------- G -------- +12V

If you take G as your "reference point", then you measure the voltages, you get -12V (with respect to G), and +12V (wrtG). So, mathematically, if G is 0, then

-12 = 0 + -12
0 = 0 + 0
+12 = 0 + 12

Take one of the other points as your reference point (say -12V) and you can just rearrange the formulae and end up by effectively sliding the scale:

0V ------- G ------- +24V

where G is now +12V (G + -12V becomes just G as +12 + -12 = 0)

0 = 12 + -12
+12 = 12 + 0
+24 = 12 + 12

So as long as G isn't connected to ground in your circuit anywhere else, you can use any of the 3 outputs as your "ground" connection - your "reference point" - and the other two voltages are relative to that, giving you G = 12V and +12V = 24V.

BUT if G is also connected to the ground of your circuit through some other means, such as the chassis, then Magic Smoke™ will escape as you are shorting -12V and G.

Every regulated split power supply that I've worked with consists internally of two independent regulated supplies that happen to be connected together at the "G" terminal (which is more often labeled "0"). Since the power supply ALSO identifies itself as +12 and +24 I felt justified in assuming that to be true in this case. But that assumption could certainly be wrong! A manufacturer and model number for the power supply would help.