"On My First Born Son" is an elegy (a poem that laments and celebrates a person who has recently died), so, yeah, death is one of its major themes. The poem attempts to offer an explanation for death, but like any poem worth reading, it goes beyond what's expected. It also tries to find something good in death. Our speaker suggests that death is an escape from a world that really isn't that pleasant, since it involves things like aging, pain, Jersey Shore, etc.
The speaker says people should "envy" those who are dead, but this is really an attempt to convince himself that his son is actually better off than he (the speaker) is. Good luck with that.
The speaker talks about the peacefulness of death. In this sense, though, death isn't really death. Actually, it is life that is really a state of death because it involves pain, sadness, suffering, aging, and all that other bad stuff. Sad, right?