Basically, the merger accepts three input signals (A, B and C) and mixes them into one output. You can control the contribution of each input signal to the output by dragging the dot inside the triangle. The merger is ideal when you want to combine a few signals that are meant to be treated as a single entity. For example, two or three synths that each provide a layer to a complex bass sound.
The splitter does the opposite: it accepts one input signal and splits it into three identical outputs. The dot inside the triangle controls the volume of each output. It's useful when you need to use the same signal in different places on your arrangement, or to combine copies of the same signal with different processing and effects. I use it a lot to distribute the kick drum to several compressors for side-chaining.
Wrong board.