Robin song is territorial advertisement rather than courtship display alone. In autumn, many robins split into separate male and female territories, each bird defending a patch of ground against all comers regardless of sex. A female holding her own winter territory sings to announce it, so the thin, wistful autumn song heard in European gardens may come from either sex.
The orange breast is the signal that matters in a dispute. Robins respond aggressively to the colour patch itself, and territorial fighting is genuinely dangerous: a substantial share of adult robin deaths in some studies is attributed to conflict with other robins. Song is the cheaper alternative, settling most boundary questions before contact.
What is still unsettled is how far the winter territorial system varies across the species' range. Robins in continental Europe are more migratory and more retiring than the famously confiding British birds, and the balance between paired winter territories and separate ones shifts with latitude and climate. The tameness itself has no single accepted explanation.