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Tizkeh lmitzvot literally means May you merit [more] mitzvot, and is used as a form of thank you among religious Jews. If someone gives you a lift home, for example, you might thank him/her by saying tizkeh/ki lmitzvot.
As it is a type of blessing, the proper response is Amen. Some add a blessing in return, Tizkeh laasot, meaning, May you merit the performance [of mitzvot].
Behind the blessing of the chance to perform more mitzvot is a fundamental principle in rabbinic thought. Ben Azzai says, One mitzvah pulls along [another] mitzvah . . . a mitzvahs reward is [another] mitzvah (Ethics of the Fathers 4).
The ideal religious life is a journey from one mitzvah to the next. As soon as you take the first step by performing a good deed, the next one comes more easily, either because of a divine reward in the form of more opportunities to do good deeds or because it is simply the way of the world that good stimulates more good.
Tizkeh lmitzvot encompasses the hope of a life full of good deeds, in which pleasure is gained from the deeds themselves and not for any reward that might result from their performance.
As for the custom of blessing one another, the Talmud teaches, The blessing of a ordinary person should never seem trivial in your eyes (Megillah 15a). In Jewish life, blessing one another is an expression not of hubris but of compassion and unity.