what does it mean on cable tv splitters when it says "-5.8dB" such as the attached pic? i have one in my basement that is a 3-way. 2 of the outputs say "-3.5db" and the third says "-7db".

 

The attenuation or signal loss caused by the splitter.

 

A splitter is a passive device, so it can only divide what it is given, and it may also have losses.

For an example (where I don't have to do any math) remember 3dB is half power, so the best an ideal 2-way splitter can go is divide one input in half to two outputs each 3dB down.