Symbolism, Imagery, Allegory
As you might imagine, the idea of a border would be an important one for a writer who had been unceremoniously kicked over one. It's true for Kundera and for some of his other dissident or roaming characters.
Jan, in particular, thinks about what it means to cross the border, but only partially because he's about to move to the United States. He thinks about it because he's aging and he's had a lot of, uh, experiences: "When things are repeated, they lose a fraction of their meaning. Or more exactly, they lose, drop by drop, the vital strength that gives them their illusory meaning. For Jan, therefore, the border is the maximum acceptable doses of repetitions" (VII.11.3).
Well, that certainly explains Jan's weariness with his old pick-up lines and his old sexual habits. But Kundera says that this isn't a full explication of the border image. For one thing, it's not an exact point in a person's life—it's more of a moving target. And it's more serious: "It takes so little, so infinitely little, for someone to find himself on the other side of the border, where everything—love, convictions, faith, history—no longer has meaning" (VII.6.5).
The border is right there with us, all the time, just waiting for our little toe to cross it. But what exactly is this border? If you're thinking death, you wouldn't be wrong, though it's a little more than that. It's a place where nothing you value in your life has meaning any longer. Where existence becomes absurd. So death it may be, but don't make the mistake of thinking that you have to be dead to be on the other side of it.