Capacitors act like water tanks. When your circuit pulls a bunch of water out of the system, the capacitor helps hold the voltage up temporarily until the power system can catch up.
For example: you may live in a city with water and water pressure. If you take a shower you affect the pressure in the municipal water system ever so slightly. If everyone turned on their shower and flushed every toilet in the city, odds are the water pressure would fluctuate quite a bit! A big water tank helps minimize these pressure fluctuations. A big cap helps minimize the voltage fluctuations on your breadboard.
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