The 100n caps are for bypassing undesired rf energy associated with stray inductances, capacitances, and rectified by diodes and transitors.
The answer above,
They are needed to supply very sudden high current to the IC. If they
are not very close to the IC the line would represent a resistance and
inductance which impededes quick current changes."
is incorrect because 100n caps won't provide a squat amount of high current.
the caps are there to filter rf. in the case of the led's, they bypass ambiant rf across the diode so that it won't be rectified - generally only needed under certain circumstances.
the caps across the power supply at the IC are crucial - they help to ensure that any rf on the power supply (ususally there is some) will bypass the IC.