Why A Yagi driven element typically has a feed point impedance well below 50 ohms, so the element is deliberately cut slightly short to make it look capacitive. A short piece of shorted parallel line or a U-shaped wire (the hairpin) placed right across the feed point acts as a shunt inductor, and that inductor plus the element's capacitive reactance forms an L-network that transforms the low resistance up to about 50 ohms. Because the stub is shorted at the far end and much less than a quarter wavelength long, it behaves purely as an inductance.
Watch out The quarter-wavelength piece of 75-ohm coax describes a different technique, the quarter-wave matching transformer or Q-section, not a beta match.
Hairpin = shorted stub = shunt inductor across the Yagi feed point.