לְמַ֨עַן יִרְבּ֤וּ יְמֵיכֶם֙ וִימֵ֣י בְנֵיכֶ֔ם עַ֚ל הָֽאֲדָמָ֔ה אֲשֶׁ֨ר נִשְׁבַּ֧ע יְהוָ֛ה לַאֲבֹתֵיכֶ֖ם לָתֵ֣ת לָהֶ֑ם כִּימֵ֥י הַשָּׁמַ֖יִם עַל־הָאָֽרֶץ׃ (ס)
그리하면 여호와께서 너희 열조에게 주리라고 맹세하신 땅에서 너희의 날과 너희 자녀의 날이 많아서 하늘이 땅을 덮는 날의 장구함 같으리라
Rashi
למען ירבו ימיכם וימי בניכם IN ORDER THAT YOUR DAYS MAY BE INCREASED AND THE DAYS OF YOUR CHILDREN — We may learn from this that if you do so, then they will be increased, but if not, they will not be increased, for the statements of the Torah may be expounded so as to derive from the negative the positive, and from the positive, the negative (Sifrei Devarim 46).
Alshekh
In order that they will be many. Even someone who was only given a few years, they will be increased for him, like Abaye, who was given a longer life due to his involvement with Torah and acts of kindness, and Binyamin the Tzadik through his charity.
Chizkuni
למען ירבו ימיכם וימי בניכם, “so that you will live long and your children will live long, etc..” Women are also obligated to put mezzuzot on their homes when no man shares the home they live in. This is logical, seeing that they too wish to enjoy long life. (Talmud, Kidushin, folio 31.)