How does electron delocalization make some free radicals more stable?

Electron delocalization increases the stability of free radicals by distributing the unpaired electron over a larger portion of the molecule rather than confining it to a single atom.1

In many chemical structures, the position of an unpaired electron can be represented by multiple, equally valid arrangements. When this occurs, the actual electronic structure is not limited to any one of these individual representations but exists as an intermediate state between them. This phenomenon is known as delocalization or resonance. According to quantum mechanics, this resonance significantly lowers the energy of the system, thereby increasing the stability of the radical and the probability of its existence.1

While most simple radicals are highly reactive and fleeting, those that possess structural features allowing for such delocalization can exist for appreciable lengths of time.21