The big cap works kind of like rolling a car that first gear went out off you get a boost to get going. All joke aside it charges up and gives the needed power.
I started doing it with them esp8266. It gives you a bigger supply for a short time. I got the idea from them supper caps.
To be fair, it's normal design practice to include a decent size electrolytic across the supply - not doing so is simply asking for trouble, particularly on anything battery powered.