This was the first version of this piece that I ever listened to. I'll be honest, I cried in my office while listening to it. Rachmaninoff is one of my favorite composers, and despite being in the same collection as Prelude in C# minor, I hadn't heard this piece before.
Elegies are considered pieces of lament for the dead, though sometimes they're used for very strong remorse or deep sadness. This piece, especially the first section, does sound like a lament for the dead. The second section is more hopeful. It feels like a reflection on the happiness with the dead loved one.
I sometimes interpret the second section as a representation of this verse:
"He shall wipe away every tear from their eyes, and death shall be no more.
Nor shall there be mourning or crying or pain any longer, for the former things have passed away." (Revelation 21:4 TLV)
At the end of days, there will be no more need of elegies. The second section reflects this promise of full restoration and happiness. Yet, the original theme comes back. We have the hope of heaven on earth, but yet we are still bound by earthly rules, including death.