Where's the battery? And how big would said battery need to be if this thing is running wi-fi in order to get "good" battery life? What good are all of these

Where's the battery? And how big would said battery need to be if this thing is running wi-fi in order to get "good" battery life? What good are all of these "things" that let you not learn to program in C or care about low level details if they get poor battery life or if they are insanely expensive? Why wouldn't I just buy an Arduino and a wi-fi/ble shield?