1:15

פרה SHIPHRAH — This was Jochebed; she bore this additional name because she used to put the babe after its birth into good physical condition (משפרת) by the care she bestowed upon it (Sotah 11b).

פועה PUAH — This was Miriam, and she bore this additional name because she used to Call aloud and speak and croon to the babe just as women do who soothe a child when it is crying (Sotah 11b).

Why is Rashi insistent that the Meyaldot are Yocheved and Miriam? All of the events regarding the Geula unfold with such precision. Hashem's promise, that they would descend, and be enslaved was fulfilled. Now the next phase, that they would emerge, is unfolding as well. This incident, defying Paroh, demonstrates why Moshe, Aharon and Miriam are the future leaders of Bnei Yisrael. This was not an isolated incident, and Yocheved, the daughter Levi, is a physical connection to the covenant with Avraham.

2:1

ויקח את בת לוי. פָּרוּשׁ הָיָה מִמֶּנָּה מִפְּנֵי גְּזֵרַת פַּרְעֹה, וְהֶחֱזִירָהּ וְעָשָׂה בָהּ לִקּוּחִין שְׁנִיִּים, וְאַף הִיא נֶהֶפְכָה לִהְיוֹת נַעֲרָה; וּבַת ק"ל שָׁנָה הָיְתָה, שֶׁנּוֹלְדָה בְּבוֹאָם לְמִצְרַיִם בֵּין הַחוֹמוֹת, וּמָאתַיִם וָעֶשֶׂר נִשְׁתַּהוּ שָׁם, וּכְשֶׁיָּצְאוּ הָיָה מֹשֶׁה בֶּן שְׁמוֹנִים שָׁנָה, אִם כֵּן כְּשֶׁנִּתְעַבְּרָה מִמֶּנּוּ הָיְתָה בַּת מֵאָה וּשְׁלוֹשִׁים וְקוֹרֵא אוֹתָהּ בַּת לֵוִי (עי' סוטה י"ב, בבא בתרא קי"ט ושמות רבה): ויקח את בת לוי AND HE HAD TAKEN TO WIFE A DAUGHTER OF LEVI — He had lived apart from her in consequence of Pharaoh’s decree that the children should, on their birth, be drowned. Now he took her back and entered into a second marriage with her, and she also physically became young again. For really she was then 130 years old — for she was born “between the walls” when they were about to enter Egypt (cf. Rashi on Genesis 46:15) and they (the Israelites) remained there 210 years, and when they left Egypt Moses was 80 years old; consequently when she became pregnant with him she was 130 years old — and yet Scripture calls her בת לוי a young daughter of Levi (Sota 12a; Bava Batra 119b).

Why it so important that Yocheved is the daughter of Levi? To show that the seeds of Geula are planted even before the Galus. The promise of the "covenant between the parts- the bris bein habesarim" is unfolding. Yocheved is a physical reminder of this.  The solutions to our problems are often times planted before the problems begin.