This is a great question. Let me answer this question in the order of the three topics - beauty, politics, and death.
According to Plato's portrayal of Socrates, beauty is a product of dialectics or we can say philosophical thinking. By using your mind you will be able to see the pure form of beauty. This comes out in Socrates' dialogue with Dotima in the Symposium. More particularly, the soul must assent to see the forms.
When it comes to politics, Socrates believes in following the laws of the city, even if they are unjust. So, in the Apology, he decides not to fight the law even if it means his life. In this context, Socrates is sentenced to death on account of corrupting the youth. When Socrates' friends want to break him out of prison, Socrates would not consider it. Instead, with poise, he drink poison and dies.
Finally, when it comes to death, Socrates is unafraid of it, because the body is a prison house for the soul. So, with death, Socrates believe that he could shed his body, which weighs him down. We can see this in Socrates's understanding of the tripartite soul.