The words “nachat ruach” mean gratification or pleasure.
In Vayikra 1:2-4 we read: “Speak to Bnei Yisrael (the sons of Israel) and say to them; If a person among you will bring a korban (sacrifice)…He shall lay his hand (perform smicha) on the head of the burnt offering and it will be favorably accepted from him to achieve his atonement.”
The Talmud, Chagiga 16b states that this teaches us that the sons of Israel perform smicha on the sacrifices but the daughters of Israel do not. Rabbi Yossi and Rabbi Shimon say: The daughters of Israel have the option to perform smicha if they wish. Abba Elazar recounted: One time we had a calf that was a Shlamim offering. We brought it to the women’s courtyard of the Temple and the women performed smicha on it. This was not because there is a requirement for women. Rather, it is in order to give “nachat ruach” (satisfaction) to the women.
The women wanted to perform the mitzvah, even though they weren’t commanded.
The Talmud, Rosh Hashanah 33a teaches that this is the source for women to perform time bound mitzvot from which they are exempt. Tosafot teach that women may even recite berachot when performing these mitzvot. That is the custom among Ashkenazi women.
Over the centuries, women have taken on positive time bound mitzvot which bring them “nachat” such as listening to the Shofar on Rosh Hashanah, shaking the lulav and sitting in the sukkah.