After the trauma of the Golden Calf, a process of forgiveness and healing begins. Moshe prays that the Divine Presence will remain in the midst of the people, and Hashem renews His covenant (Shemot 34:10). As Ramban comments, since the sin of the Calf abrogated the first covenant, there is a need to renew it here, which is why the passage is focused on idolatry.

Thus, after the prohibitions of partaking from idolatrous sacrifices, and repeated warnings against idolatry in general, Hashem continues with a number of familiar commandments:
Molten gods you shall not make for yourself.
Observe the Festival of Matzot: for seven days you shall eat matzot, as I commanded you, at the appointed time in the month of spring (standing grain), for in the month of spring (standing grain) you went forth from Egypt.
Every first issue of a womb is Mine …
They shall not appear before Me empty-handed.
Six days shall you work and on the seventh day shall you refrain. From plowing and harvesting shall you refrain.
And the Festival of Weeks shall you make for yourself at the first offering of the wheat harvest. And the Festival of the In-gathering shall be at the changing of the year.
Three times a year shall all your males appear before the Lord Hashem, G-d of Israel. For I shall expel nations before you and broaden your boundary; no man shall covet your land when you ascend to appear before the Presence of Hashem, your G-d, three times a year.
You shall not slaughter the blood of My sacrifice while in possession of leaven; and you shall not leave overnight the sacrifice of the Pesach sacrifice until morning.
The first of your land’s first-fruits shall you bring to the House of Hashem, your G-d.
You shall not cook a kid in its mother’s milk (34:17-26).

Abravanel (Don Yitzchak Abravanel, 1437-1508) asks: Since most of these commandments were taught earlier (23:10-23), why are they repeated now? He answers:
“Israel thought that He would impose difficult acts on them so as to cleanse them of their transgression. …But since Hashem, may He be blessed, desires kindness, He did not do so with Israel. When He was reconciled with them for the grave iniquity which they committed, He did not burden them with harsh and heavy commandments.”
Instead of creating stringent acts of penance, Hashem reminded them to renew their commitment to the same mitzvot as before their sin.

But, why these mitzvot? And why the emphasis on the Pilgrimage Festivals?

One approach (Da’at Mikra) relates to the events surrounding the Golden Calf itself: Since the Israelites proclaimed a festival in honor of the calf (32:5-6, 19), the Torah reminds them to celebrate Hashem’s festivals only.

Hirsch (Rabbi Shimshon Raphael Hirsch, 1808-1888), on the other hand, sees the Golden Calf as symptomatic of the ever-present temptation of idolatry, which regards the forces of nature as absolute and inexorable. Rather, through these commandments, Hashem teaches:
“Nature does not stand between you and Me, but you stand between Nature and Me. It is according to your behavior towards Me that everything that flourishes and breathes for you in your sphere, lives or dies, flourishes or withers, dies off, or endures.”
Every encounter with natural forces first requires submission to the Will of Hashem. Consequently, we are commanded to take the three agricultural milestones – ripening, harvest, in-gathering – out of the realm of Nature, where man is buffeted by forces beyond his control, and transform them into festivals of Man’s spiritual growth in obedience to Hashem. Furthermore, He controls those forces, in response to your obedience, for your sake. This occurred throughout the Exodus and would be repeated, as they would not have to fear invasion during the pilgrimages. Each of these mitzvot educates towards unmediated relationship between Man and G-d.

Sforno (R. Ovadia ben Yaakov Sforno, c. 1470-c.1550) sees a strong parallel between these commandments and recent events. First came Pesach. Then the commandment of the firstborn (13:1-2, 11-15) was given, because the firstborn were saved during the tenth plague. Next came Shabbat (16:22-30; see also Rashi on 15:25) and the seventh shemittah year, which was previously linked with Shabbat (23:10-12).

The people subsequently made the Golden Calf in order to benefit themselves. Therefore the Torah prohibits molten gods here, which:
“are talismans [see The Guide for the Perplexed I 63], made at certain hours in conjunction with certain stars. Therefore they are molten, so that all the parts of those symbols would combine simultaneously. Those who made them thought they would thereby attain their material and bodily needs. Perhaps one might think that this was not rebellion against G-d, may He be blessed, since he did not accept it upon himself as a god; still it is contrary to His will, for He wants His worshipers to turn for help to no deity but Him, as it says, We do not know what to do, but our eyes are upon You (Divrei HaYamim II 20:12).”

During the three agricultural events, says Sforno, people imagine they will have success if they but obey the dictates of nature; but obeying Hashem is far more decisive. Thus, the passage continues with Shavuot and Sukkot, followed by one commandment common to all the festivals― making the pilgrimage. Finally, there are commandments specific to each festival: the particulars of Pesach; the first-fruits brought during Shavuot; and not cooking a kid in milk, which heathens often did when the animals were born, at Sukkot time (see Ramban and Malbim, R. Meir Leib ben Yechiel Michael, 1809-1877). All the mitzvot in this passage are restated in the same order that they were first presented to Israel.

After the near-rupture in relations between Hashem and Israel, He takes them, as it were, “down memory lane,” recapping the events of the past months. It is as if Hashem is saying, “Look how far we’ve come together. We have had some serious differences, but we must not give up on each other.”