The capacitor is needed to act as a local reservoir of power to the PIC. Although it may seem adequate to simply connect supply wires, you have to consider that each wire has resistance and inductance, both increasing the impedance of the supply. When the PIC operates, many thousand internal gates and transistors switch on and off and as they do so, they each need a tiny but significant amount of current. Collectively, the amount of current starts to become important and is what you measure as the current drawn into the VDD supply lines. Because there are so many circuits switching at different times, the current waveform is very complex, in fact it looks like high frequency random noise. Without the decoupling capacitor the impedance of the supply wires allows the VDD line to convert the current into a voltage variation which in turn upsets the internal PIC circuits. When the capacitor is fitted, it provides a source of current right up to the PIC itself so the supply wiring becomes far less critical.
Your circuit might work without the capacitor but you may find it unreliable and more prone to interference or voltage variations than it should be. Good practice is to use two decoupling capacitors, one of a few uF to help with the slower current variations and one of around 100nF to help at higher frequencies. In general, larger capacitors, particularly electrolytic types, lose effectiveness as the frequency increases while lower value ceramic types work the other way around. If you connect both in parallel across VDD and VDD you get the best of both properties.
Brian.