Plain English Meaning
When you need to turn from one route onto another, you don't wait until you're on top of the new route to start turning -- you'd fly straight past it. Instead, you pick a radial a little before the turn point and start the turn there. That earlier radial is your cue to begin turning so you roll out neatly on the new course.
Full Definition
A lead radial is a VOR radial used as an early cue to begin the turn from one airway or course onto another, allowing the aircraft to roll out smoothly on the new course rather than overshooting it. The pilot starts the turn when the lead radial is reached, not when the new course is reached, because the aircraft needs distance and time to complete the turn at its current groundspeed and bank angle.
Context Anchor
Seen in instrument flying when using VOR , especially when joining, leaving, or turning between published .