If a man says to a woman, “You are halachically engaged to me with the peruta (a small coin) that I’m handing you right now, on the condition that I have a beit kor of land,” a beit kor is a certain measurement of land. He is engaged to her. If he has it—if he owns that piece of land—he has to have two witnesses who can testify that he owns that piece of land.
If a man says to a woman, “You are halachically engaged to me on the condition that I have a beit kor of land in a certain place,” if he has a beit kor of land, he is halachically engaged. They are engaged. But if not, she is not halachically engaged.
If he says to her, “You are halachically engaged to me on the condition that I’m going to show you a beit kor of land,” “show you” is a vague term. So we say he is engaged to her if he shows her a beit kor of land that belongs to him. But if he shows her a piece of land in the open field that doesn’t belong to him, she’s not engaged even if he’s renting it. The general understanding of “I’m going to show you a piece of land that’s this big” is that he’s talking about his. He’s talking about land that he owns. So that’s what we’re trying to show with this last part of the Mishnah.