The strings are run through drill holes in the bridge and knotted with a bow tie.
As with many guitars, the strings of some Ukuleles end in pins that are fixed behind the bridge with ball-ends.
Changing strings on an ukulele with pin bridge
The ends of the strings are fed through slots in the bridge and fixed with knots. The tension of the strings keeps them in place. Changing strings is therefore straightforward; but when tension is reduced too much, the strings can pop out from the bridge.