In Exo. 12:12-13, it is written,
12 For I will pass through the land of Egypt this night, and I will smite all the firstborn in the land of Egypt, both man and beast, and I will execute judgment against all the gods of Egypt. I am Yahveh. 13 And the blood shall be your sign upon the houses where you are. And when I see the blood, then I will [וּפָסַחְתִּי] over you, and the destroyer’s plague shall not be among you when I smite the land of Egypt.
יב וְעָבַרְתִּי בְאֶרֶץ מִצְרַיִם בַּלַּיְלָה הַזֶּה וְהִכֵּיתִי כָל בְּכוֹר בְּאֶרֶץ מִצְרַיִם מֵאָדָם וְעַד בְּהֵמָה וּבְכָל אֱלֹהֵי מִצְרַיִם אֶעֱשֶׂה שְׁפָטִים אֲנִי יַהְוֶה יג וְהָיָה הַדָּם לָכֶם לְאֹת עַל הַבָּתִּים אֲשֶׁר אַתֶּם שָׁם וְרָאִיתִי אֶת הַדָּם וּפָסַחְתִּי עֲלֵכֶם וְלֹא יִהְיֶה בָכֶם נֶגֶף לְמַשְׁחִית בְּהַכֹּתִי בְּאֶרֶץ מִצְרָיִם
The narrative is a bit complex; however, the general idea is as follows. The Israelites sacrifice the Pesach offering.1 The blood of this Pesach offering is caught in a basin, and a bunch of hyssop is used to apply the blood to the lintel and two side-posts of the Israelite homes.2 Yahveh via Moses tells the Israelites that the blood applied to their door-posts in the specified manner will be “your sign” [לָכֶם לְאֹת].3 Yahveh sees this sign and does not allow the destroyer [מַשְׁחִית] to come unto their houses to plague the Israelites.4 The destroyer [הַמַשְׁחִית] is an entity that is to plague [לִנְגֹּף]5 with a plague [נֶגֶף]6 every firstborn in Egypt where Yahveh does not see the sign of the blood upon the door-posts. In fact, the plague is referred to as “the destroyer’s plague” [נֶגֶף לְמַשְׁחִית].7
Footnotes
1 Exo. 12:28 cf. Exo. 12:6, 12:21
2 Exo. 12:28 cf. Exo. 12:7, 12:22
3 Exo. 12:23 cf. Exo. 12:13
4 Exo. 12:23 cf. Exo. 12:13
5 Exo. 12:23
6 Exo. 12:13
7 Exo. 12:13. Granted, Carl Friedrich Keil (p. 19) commented, “...there is no article with למשׁחית.” He understands נֶגֶף לְמַשְׁחִית as meaning “plague to destroy.” However, the article would be indicated by a dagesh (small dot) within the מ, like so מּ, and such [Masoretic] vowel pointing would not have been part of the original manuscript.
Since it is written that Yahveh Himself will “pass through” (note: this is the verb עָבַר avar) the land of Egypt and smite all the firstborn in the land of Egypt, but this is actually accomplished via “the destroyer” which plagues the firstborn of Egypt with a plague, we can reasonably conclude that the destroyer is Yahveh’s agent of destruction. Yonatan ben Uzziel suspects as much, as he interpreted the Hebrew into Aramaic as מלאכא מחבלא (“the destroying angel”) in his targum.8
Footnotes
8 Targum of Yonatan ben Uzziel, Exo. 12:23
Therefore, we have Yahveh and Yahveh’s destroyer. These are two separate entities. The latter is Yahveh’s agent which executes judgment upon Egypt and plagues the firstborn with the plague of death. A similar entity encountered in 1 Chr. 21:15 is referred to as “the destroying9 angel” [לַמַּלְאָךְ הַמַּשְׁחִית] and executes judgment and destruction at God’s behest.
Footnotes
9 or “destroyer”
Meredith G. Kline wrote,10

Footnotes
10 Kline, p. 499
With that being said, it’s a bit easier to understand what is occurring during the final plague. As the destroyer is passing through Egypt, it is plaguing the firstborns with the plague of death, thus killing them. However, the destroyer is impeded from entering the houses of the Israelites only because Yahveh Himself sees the sign of the blood on their door-posts. When Yahveh sees this sign, He does not “pass over” the Israelites’ houses. If Yahveh were to simply pass over their houses, it would not impede the destroyer who could enter the houses after Yahveh passed over. (Therefore, the verb פָּסַח pasach does not really mean “pass over” when translated into English.) Yahveh, upon seeing the sign of the blood upon the door-posts, then covers (or hovers over, protects) these houses. When Yahveh covers the houses of the Israelites, the destroyer is not allowed to come unto the houses to plague the Israelites. Yahveh Himself is providing divine protection over these houses until all the firstborns of Egypt without divine protection have been plagued and killed by the destroyer.
References
Keil, Carl Friedrich. Commentary on the Old Testament. 1900. Reprint. Trans. Martin, James. Vol. 1. Grand Rapids: Eerdmans, 1986.
Kline, Meredith G. “The Feast of Cover-Over.” Journal of the Evangelical Theological Society. 37/4 (1994): 497–510.