Antonio has followed Sebastian into the city despite the danger. He gives Sebastian his purse for safekeeping and arranges to meet him at the Elephant.
Antonio has followed Sebastian through the city, despite knowing that Illyria is dangerous for him: he has a history of conflict with Orsino's people and is effectively a wanted man in the city. Sebastian wants to go sightseeing; Antonio explains he cannot walk openly through the streets without risk.
Antonio gives Sebastian his purse for safekeeping, since Sebastian may want to buy something while exploring. They agree to meet later at an inn called the Elephant. Antonio goes to find lodgings; Sebastian goes to look at the city.
This brief scene carries weight disproportionate to its length. Antonio's decision to give Sebastian his purse is a gesture of complete trust: he is handing over his money to someone he has known for a relatively short time, in a city where he himself cannot move freely. The purse will become a central object later, when Antonio is arrested and asks Viola (whom he mistakes for Sebastian) to return it, and she cannot.
Antonio's language about following Sebastian continues the devotion established in Act 2, Scene 1. He says he could not stay behind; his desire for Sebastian's company was "more sharp than filed steel." He frames the risk he is taking as something he chooses willingly, as an expression of love rather than obligation. The word "desire" continues to carry more weight than ordinary friendship would require.
Sebastian's behaviour in contrast is easy and self-directed. He wants to see the sights. He is not indifferent to Antonio, but his attention is already moving toward the city rather than backward toward his companion. The asymmetry that was established in Act 2, Scene 1 continues here: Antonio's feeling is intense; Sebastian's is comfortable but not equivalent.
The Elephant as a meeting place is a small but vivid detail. It grounds the scene in a realistic urban setting, gives the audience a named location to track later, and reinforces that Illyria, despite being a comic world, has streets, inns, and the ordinary machinery of a real city.