Why you need a DI box for your electric guitar
Why can't you plug an electric guitar into a mixing console input without using a DI box or preamp?
The answer is that the electric guitar (unless it has a built-in preamp)has a 'high impedance' output. This means that although the pickup can produce a reasonably strong voltage, its current drive capability is limited.
The best way to think of this is as the signal being carried by a small number of electrons. Each electron is doing its best, but there are only a few of them.
The microphone and line inputs of the mixing console are of low and medium impedance respectively. This means that they demand more current than the guitar is able to supply. The result is a weakened signal, noticeably lacking in high frequency content.
The DI (direct inject) box or preamp boosts up the current of the signal so that it is meaty enough to drive the console input.
So why can't console inputs be high impedance? The answer is that this is not optimal. A high impedance signal is prone to noise and interference. High impedance signals are only used where necessary, and for preference the cable run should be short.