This line is spoken by Edmund at the very end of Scene 3 in Act 3. It is a wonderful closing line. It expresses succinctly what the play is really all about--and what the world is all about. Shakespeare's play dramatizes a few examples of how one generation is relentlessly and remorselessly supplanted by the generation behind it, a natural process which cannot be changed. Everywhere and at all times the generation that owns the property and runs the world is growing older and weaker. We do not see this happening as quickly and as completely as it does in Shakespeare's famous tragedy, but it is happening every minute of every day. When a top executive of a corporation retires, some younger person is moved up into his spot, leaving a vacancy which will be filled by someone coming up behind him--and that person will likely leave an entry-level vacancy to be fill by a young newcomer fresh out of college. Whenever a person dies, others, usually younger people, take over his home and his possessions, not realizing that someday the same thing will be happening to them. A good example of this is to be found in Leo Tolstoy's bitterly truthful story "The Death of Ivan Ilyich."
So on receiving the news of Ivan Ilych's death, the first thought of each of the gentlemen in that private room was of the changes and promotions it might occasion among themselves or their acquaintances.
"I shall be sure to get Shtabel's place or Vinnikov's," thought Fedor Vasilievich. "I was promised that long ago, and the promotion means an extra eight hundred rubles a year for me besides the allowance."
"Now I must apply for my brother-in-law's transfer from Kaluga," thought Peter Ivanovich. "My wife will be very glad, and then she won't be able to say that I never do anything for her relations."
These are the true thoughts of Ivan Ilyich's friends and colleagues immediately after hearing the news of his death. There are only so many niches in the world, and when a niche becomes vacant it will quickly be filled by a newcomer. It is part of the universal struggle for survival.