While there are various other answers to this question, I will highlight a few of them:
One simple answer is that Moshe wanted to see the land, and this is what Rashi (Devarim 3:27) suggests:
וראה בעיניך – בקשתה ממני: ואראה את הארץ הטובה (דברים ג׳:כ״ה), אני מראה לך את כולה, שנאמר: ויראהו י״י את כלא הארץ (דברים ל״ד:א׳).
וראה בעיניך [LIFT UP THINE EYES …] AND SEE IT WITH THINE EYES – Thou didst request of Me, (v. 25) "Let me see the good land"; I will let thee see the whole of it (not the good territory alone), as it is said, (Deuteronomy 34:1) "And the Lord showed him all the land" (cf. Sifrei Bamidbar 135). (Alhatorah translation)
Ralbag there elaborates and provides potential reasons why Moshe would have wanted to see it, namely that Moshe had heard a good report of it, and wanted to see some of that firsthand.
Another answer (given by Shadal to Bamidbar 27:13, and by Ibn Caspi to Devarim 3:27) is that this was a way of showing Moshe that he did not waste his efforts in bringing the nation to this point.
Minchas Yehuda to Devarim 3:27 provides a very original thought, noting that God had sworn that none of those that despised him would see the land (Bamidbar 14:23). Therefore, to make sure that no one would claim that Moshe was part of that evil group, God took him to see the land