The Hebrew phrase וַיִּשְׁמְעוּ אֶת-קוֹל יַהְוֶה אֱלֹהִים מִתְהַלֵּךְ בַּגָּן לְרוּחַ הַיּוֹם (vayyishmeʿu et-kol Yahveh elohim mithallekh bagan leruach ha-yom) essentially translates into English as the following:
And they heard the sound of Yahveh God walking in the garden in the wind of the day...
The Hebrew word רוּחַ (ruach) is most often translated as “spirit,” but it is also translated often as “breath”1 and “wind.”2
1 Job 15:30: “and by the breath (רוּחַ) of his mouth shall he go away”
2 Gen. 8:1: “And God made a wind (רוּחַ) pass over the earth, and the waters abated”
In the instance in Gen. 3:8, it is referring to the “wind of the day”—the evening when the sun begins to set and the breeze may blow, causing it to be relatively cooler than “the heat of the day.”3 A somewhat similar phrase occurs in Songs 2:17,4 “until the day blows”—from the Hebrew phrase עַד שֶׁיָּפוּחַ הַיּוֹם (ad sheyyafuach ha-yom).
3 כְּחֹם הַיּוֹם (kechom ha-yom): cf. Gen. 18:1; 2 Sam. 4:5; also, חֹם הַיּוֹם (chom ha-yom): cf. 1 Sam. 11:11
4 Songs 2:17 LXX: «ἕως οὗ διαπνεύσῃ ἡ ἡμέρα»—“until the day blows through”; cf. Songs 4:6
An English translation of Gesenius states,5
A later revised and edited German text based on Gesenius’ lexicon states,6
Gen. 3:8 the blowing of the day, that is, the evening, a few hours before sunset when a more refreshing wind usually blows. (cf. Songs 2:17, 4:6)
5 Gesenius on רוּחַ, p. 760
6 This is the 16th edition published in 1915 (cited below). In thought, it is not much different from the 1st edition German text published in 1812 (Vol. 2) (also cited below). However, there are minor differences, as seen below in the 1st edition:
To that (i.e., the meaning “wind”) also belongs [the phrase] רוּחַ הַיּוֹם Mos[es] 3:8 (i.e., Gen. 3:8). The blowing of the day, that is, the evening, because in the Orient, a more refreshing wind usually blows a few hours before sunset. (cf. Songs 2:17, 4:6, and [Jean] Chardin[’s] Voyage en Perse, Book IV, Section 13.
Gesenius, Heinrich Friedrich Wilhelm. Gesenius’s Hebrew and Chaldee Lexicon to the Old Testament Scriptures. Trans. Tregelles, Samuel Prideaux. London: Bagster, 1860.
Gesenius, Heinrich Friedrich Wilhelm. Hebräisch–Deutsches Handwörterbuch über die Schriften des Alten Testaments. 1st ed. Vol. 2. Leipzig: Vogel, 1812.
Gesenius, Heinrich Friedrich Wilhelm. Hebräisches und aramäisches Handwörterbuch über das Alte Testament. Ed. Bulh, Frants. 16th ed. Leipzig: Vogel, 1915.