(כח) וְשֶׂ֣רֶט לָנֶ֗פֶשׁ לֹ֤א תִתְּנוּ֙ בִּבְשַׂרְכֶ֔ם וּכְתֹ֣בֶת קַֽעֲקַ֔ע לֹ֥א תִתְּנ֖וּ בָּכֶ֑ם אֲנִ֖י ה'׃
(28) You shall not make gashes in your flesh for the dead, or incise any marks on yourselves: I am the LORD.
(2) וכתבת קעקע [NOR SHALL YE IMPRESS] ANY WRITING BY ETCHING [UPON YOU] — i. e. a writing engraved (more lit., dug into) and sunk into the flesh and which can never be erased because it is pricked in with a needle and remains black forever.
Rashi says that etching is a writing that is in the skin with a needle and is permanent.
Iben Ezra says that tattoo here is connected to the first part of the pasuk about not cutting yourself for the dead. People used to give themselves tattoos to remember the dead and this is also a prohibition against that practice.
מתני׳ הכותב כתובת קעקע כתב ולא קעקע קעקע ולא כתב אינו חייב עד שיכתוב ויקעקע בידו ובכחול ובכל דבר שהוא רושם ר"ש בן יהודה משום ר' שמעון אומר אינו חייב עד שיכתוב שם את השם שנאמר (ויקרא יט, כח) וכתובת קעקע לא תתנו בכם אני ה':
The Mishnah is telling us the punishments for the different levels of offenses.
The amorites used to make tattoos on the basis of superstitions. This is another reason that we cannot have tattoos- you cannot have superstitions.
If one gets a tattoo he is trying to perfect his body. When one does this he is basically saying that Hashem made a mistake and what he created, isn't perfect.
You shouldn't get tattoos or anything related to that because you are holy to Hashem.
You can't cut yourself or get tattoos because the Amorites used to do it.
(יא) כְּתֹבֶת קַעֲקַע הָאֲמוּרָה בַּתּוֹרָה הוּא שֶׁיִּשְׂרֹט עַל בְּשָׂרוֹ וִימַלֵּא מְקוֹם הַשְּׂרִיטָה כָּחל אוֹ דְּיוֹ אוֹ שְׁאָר צִבְעוֹנִים הָרוֹשְׁמִים. וְזֶה הָיָה מִנְהַג הָעַכּוּ''ם שֶׁרוֹשְׁמִין עַצְמָן לַעֲבוֹדַת כּוֹכָבִים כְּלוֹמַר שֶׁהוּא עֶבֶד מָכוּר לָהּ וּמֻרְשָׁם לַעֲבוֹדָתָהּ. וּמֵעֵת שֶׁיִּרְשֹׁם בְּאֶחָד מִדְּבָרִים הָרוֹשְׁמִין אַחַר שֶׁיִּשְׂרֹט בְּאֵי זֶה מָקוֹם מִן הַגּוּף בֵּין אִישׁ בֵּין אִשָּׁה לוֹקֶה. כָּתַב וְלֹא רָשַׁם בְּצֶבַע אוֹ שֶׁרָשַׁם בְּצֶבַע וְלֹא כָּתַב בִּשְׂרִיטָה פָּטוּר עַד שֶׁיִּכְתֹּב וִיקַעֲקֵעַ שֶׁנֶּאֱמַר (ויקרא יט כח) "וּכְתֹבֶת קַעֲקַע". בַּמֶּה דְּבָרִים אֲמוּרִים בְּכוֹתֵב אֲבָל זֶה שֶׁכָּתְבוּ בִּבְשָׂרוֹ וְקִעְקְעוּ בּוֹ אֵינוֹ חַיָּב אֶלָּא אִם כֵּן סִיֵּעַ כְּדֵי שֶׁיַּעֲשֶׂה מַעֲשֶׂה. אֲבָל אִם לֹא עָשָׂה כְּלוּם אֵינוֹ לוֹקֶה:
(11) The etched-in writing against which it is spoken of in the Torah is, not to make an incision in one's flesh and fill in the incision with paint, or ink, or any other dyes which enface. This was an idolatrous custom, to make themselves to idolatry, proclamatory that every one of them is a sold slave to it, and indentured in its service. And, from the moment one will enface with any kind of dye which enfaces, after making an incision in any place of the body, whether it be done by man or by woman, he or she, is striped. If one wrote but did not enface with dye, or if he did enface with dye but did not write in the incision, he is not guilty; for he must do both, write by incision and etch-in with dye, even as it is said: "And any etched-in writing shall you not fix on yourselves" (Lev. 19. 28). This is to say against the one who does the writing, but he who upon whose flesh the etched-in writing was done is not guilty save if he assisted in a manner to constitute it an overt act; but if he contributed nothing to the work itself he is not striped.14Makkot, 21b; Sifre, Lev. Ch. 19. C. G.
Tattoos are prohibited because they used to be connected to idols and idols worshiping.
(ג) מדיני המצוה. מה שאמרו זכרונם לברכה (רמב''ם ע''ז י''ב י''א), שכל מקום שבגוף, בין מגלה, בין מכסה בבגדים, בכלל אסור זה. ויתר פרטיה, בסוף מסכת מכות.
(3) From the laws of the commandment is that which they, may their memory be blessed, said (Mishneh Torah, Laws of Foreign Worship and Customs of the Nations 12:11) that every place on the body - whether it is revealed, or whether it is covered by clothes - is included in this prohibition. And the rest of its details are at the end of Tractate Makkot.
All parts of the body are included in this prohibition.