He's talking about his own childhood dreams. It's like you asking your friends about their dreams before you go on to explain yours. He's trying to get them to connect with him emotionally by bringing up their own childhood dreams. That's an usual tactic people use to persuade others. The only person in that room who shared a similar dream is, perhaps, Crocodile.
Mihawk's gonna enter the throne wars one way or another, and he along with Crocodile will make Buggy a primary PK candidate. Given how well this gag is going, Buggy may actually end up being ahead of Blackbeard, and it'll happen via Mihawk and Crocodile.
If Mihawk's actually interested in being PK, then it creates a direct conflict b/w Luffy's and Zoro's dreams as that makes Mihawk a direct opponent to Luffy as he's the main guy from their crew and he aims to take Luffy's head. To avoid that, Oda needs to make Mihawk neutral while still involving him in the throne wars, and that'll only happen if Mihawk has no interested in being the PK.