(10) for you must distinguish between the sacred and the profane, and between the unclean and the clean;
The basic requirement for ritual purity is expressed in Lev 10:10 which identifies the binaries of holy/common and clean/unclean. However, there is no archaeological evidence for the construction of ritual baths until the mid 2nd cent. BCE. But this doesn't mean that ritual purity was not practiced before that time.
Where else in the Tanak does the binary clean/unclean occur together?
(Hint: click on the text and look for connections)
The sections of Lev 11–15 and Num 5 and 19 explain the main causes of ritual impurity.
Can you list the main causes of impurity?
While this text uses the term מקוה, it means "hope" and not "gathering." Mishnah Yoma 8:9 connects the two concepts below.
(ט) הָאוֹמֵר, אֶחֱטָא וְאָשׁוּב, אֶחֱטָא וְאָשׁוּב, אֵין מַסְפִּיקִין בְּיָדוֹ לַעֲשׂוֹת תְּשׁוּבָה. אֶחֱטָא וְיוֹם הַכִּפּוּרִים מְכַפֵּר, אֵין יוֹם הַכִּפּוּרִים מְכַפֵּר. עֲבֵרוֹת שֶׁבֵּין אָדָם לַמָּקוֹם, יוֹם הַכִּפּוּרִים מְכַפֵּר. עֲבֵרוֹת שֶׁבֵּין אָדָם לַחֲבֵרוֹ, אֵין יוֹם הַכִּפּוּרִים מְכַפֵּר, עַד שֶׁיְּרַצֶּה אֶת חֲבֵרוֹ. אֶת זוֹ דָּרַשׁ רַבִּי אֶלְעָזָר בֶּן עֲזַרְיָה, מִכֹּל חַטֹּאתֵיכֶם לִפְנֵי יְיָ תִּטְהָרוּ (ויקרא טז), עֲבֵרוֹת שֶׁבֵּין אָדָם לַמָּקוֹם, יוֹם הַכִּפּוּרִים מְכַפֵּר. עֲבֵרוֹת שֶׁבֵּין אָדָם לַחֲבֵרוֹ, אֵין יוֹם הַכִּפּוּרִים מְכַפֵּר, עַד שֶׁיְּרַצֶּה אֶת חֲבֵרוֹ. אָמַר רַבִּי עֲקִיבָא, אַשְׁרֵיכֶם יִשְׂרָאֵל, לִפְנֵי מִי אַתֶּם מִטַּהֲרִין, וּמִי מְטַהֵר אֶתְכֶם, אֲבִיכֶם שֶׁבַּשָּׁמַיִם, שֶׁנֶּאֱמַר (יחזקאל לו), וְזָרַקְתִּי עֲלֵיכֶם מַיִם טְהוֹרִים וּטְהַרְתֶּם. וְאוֹמֵר (ירמיה יז), מִקְוֵה יִשְׂרָאֵל יְיָ, מַה מִּקְוֶה מְטַהֵר אֶת הַטְּמֵאִים, אַף הַקָּדוֹשׁ בָּרוּךְ הוּא מְטַהֵר אֶת יִשְׂרָאֵל:
(9) One who says, "I will sin, and then repent, I will sin [again], and then repent," will not receive an opportunity to repent; [for one who says] "I will sin, and Yom Kipur will atone," Yom Kippur will not atone. Yom Kippur atones for transgressions between a person and God, but for a transgression against one's neighbor, Yom Kipur cannot atone, until he appeases his neighbor. Thus R. Eleazar ben Azariah expounds the text, "From all your sins before the Lord shall ye be clean": For transgressions between a person and God, Yom Kippur atones, for transgressions against one's neighbor, Yom Kippur cannot atone, until he appeases his neighbor. R. Akiva says, Happy are you, Israel! Before whom are you purified, and who purifies you [of your transgressions]? Your Father Who is in heaven. For it is said, "Then will I sprinkle clean water upon you, and ye shall be clean"; and it is also said, "The ritual bath [lit. Hope] of Israel is the Lord"; even as a ritual bath purifies the unclean, so does the Holy One, Blessed be He, purify Israel.
Here, Rabbi Akiva interprets Jer 14:8 with a wordplay on the word מקוה which also means "hope."
Photo courtesy of https://www.bibleplaces.com/.
During the late Second Temple period, ritual baths proliferated. This is a photo of a ritual bath at the Temple Mount southern steps.
Today, one can tour these ritual baths in the Jerusalem National Park. More about this park is available at this link:
http://shavuot.antiquities.org.il/Article_eng.aspx?sec_id=25&subj_id=240&id=4249
Ritual baths are still used today. See the following news link about a community in Pennsylvania that has recently built a ritual bath center. https://www.usnews.com/news/best-states/pennsylvania/articles/2018-04-28/mikvah-building-boomlet-as-jewish-ritual-baths–open