Life, Death, and Peace
The situation of the poem is that Donne is dying. He has some illness or disease which his doctors are studying (like cosmographers / geographers study a map) by closely examining his body as he lies in bed. They have told him he is going to die.
Donne makes an extended play or comparison between life and death on the one hand, and what you might call geography on the other hand. Sometimes it is punning, as when he says 'by these straits to die' - straits are a narrow passage of water, difficult and dangerous for a ship to navigate, and so we sometimes say when we are in a difficult situation.
Sometimes he uses west (where the sun sets) to symbolise his death, and so by contrast the east or sunrise symbolises the beginning of life, or new life. And he runs with this theme a little, wondering where he really belongs. So he begins to play with the idea of death and resurrection - for there to be a resurrection, there must first be a death, as there was with Christ.
Overall, although he knows he faces a difficult passage in the near future (his physical death) he is also confident that at the far side of that experience, because of the salvation Christ brought, he can look forward to his own resurrection, and so he is ultimately at peace and can rest in God. As a priest he has had to preach this truth to others who were dying, when he attended them, now he preaches it to himself. He plays on the idea of Christ the King, too and Donne feels the thorns (the pains of his illness) and they reflect the crown of thorns that was mockingly placed on Christ's head in preparation for his crucifixion, but looks forward to the true crown with which the triumphant, resurrected and ascended Christ is crowned in heaven, and which is reflected in the crowns given to Christ's faithful followers when they too finally reach glory.
The language of the poem is dense with biblical allusion, but...