Exode 2:1

Your decree is harsher than פַּרְעֹה. Whereas Pharaoh issued a decree [only] against the males, you [issued a decree] against the females as well [for none will be born]

And Amram, a man of the tribe of Levi, went and returned to live in marriage with Jokeved his wife, whom he had put away on account of the decree of Pharoh. And she was the daughter of a hundred and thirty years when he returned to her; but a miracle was wrought in her, and she returned unto youth as she was, when in her minority she was called the daughter of Levi.

AND THERE WENT A MAN OF THE HOUSE OF LEVI. Our Rabbis have said that he went after the advice of his daughter., i.e., “went” after the advice of his daughter and remarried his divorced wife. See also further on in the text for a reference to a prophecy Miriam made at that time. Rabbi Abraham ibn Ezra said that the Israelites dwelled in many cities, and this woman Jochebed lived in another city. [This would explain the term “went” in the above verse, i.e., he went to another city for his wife.] But what need is there for Scripture to mention this?
In my opinion Scripture uses the term “went” because this man paid no heed to Pharaoh’s decree and took to himself a woman to beget children. Such is Scripture’s way of speaking of anyone who prompts himself to do something new. Thus: And Reuben went and lay with Bilhah; So he went and took Gomer the daughter of Diblaim; Come, and let us sell him to the Ishmaelites; Come, and let us smite him with the tongue; Come now, and let us reason together. Similarly this man Amram alerted himself and married a daughter of Levi.
The reason Scripture does not mention the name of the man nor the name of the woman he married is to avoid tracing their genealogy and mentioning who their fathers and their fathers’ fathers were up to Levi. At this point, Scripture desires to shorten the subject until the birth of the redeemer takes place, and after that, in the second seder,. (A seder is the weekly portion of the Torah read in the synagogue at the Sabbath morning services.) Specifically, Moses’ genealogy is found in Seder Va’eira, Chapter 6, Verses 16-20. He traced the genealogy even of other tribes, Verses 14-15). on account of Moses.
In line with the simple meaning of Scripture, i.e., that this was a first marriage [and not a remarriage as stated above], there is no significance in its being mentioned earlier or later in the chapter. This marriage took place before Pharaoh’s decree [that all male Hebrew children be killed], and she gave birth to Miriam and Aaron. After that, Pharaoh decreed, Every son that is born, ye shall cast into the river, and then she gave birth to this goodly son Moses. Scripture did not mention the birth of Miriam and Aaron inasmuch as there was nothing new about them. However, in the opinion of our Rabbis, this was a remarriage, since Amram separated from his wife in consequence of Pharaoh’s decree and then took her back on account of his daughter’s prophecy. He made her a wedding and placed her in the litter, while Miriam and Aaron danced about them in their joy because through this marriage, Israel would be redeemed [from Egypt]. Even though Aaron was young [at that time], G-d put gladness in his heart for this occasion, or possibly his sister Miriam taught him.

וילך איש מבית לוי, a reference to Amram.

ויקח את יוכבד בת לוי, She had been born for Levi in Egypt (Numbers 26,59). He married her many years before Moses was born, for Aaron was 83 years old when he appeared before Pharaoh with Moses who was 80 years old at the time.