A two-transistor LED flasher circuit operates as a flip-flop, where the transistors alternately switch on and off, causing the LEDs to blink. The timing of the switching is influenced by the charging and discharging of a capacitor, which affects the voltage across the transistors. As one transistor turns on, it allows current to flow through the LED, while the other transistor turns off, preventing current flow through its LED. This cycle continues, creating the flashing effect. Understanding the interplay between the capacitor and transistors is key to grasping how the circuit functions.