The verb “tira’u” in this verse is typically translated “fear,” but there’s no obligation to cower in terror from one’s parents. In fact, that would probably be a bad thing. I think that when applied to God, the tern yirah (“fear”) is better translated as “awe” and when applied to one’s parents, it’s better rendered as “deference.” Mitzvah #33 is the obligation to “honor” one’s parents; that refers to things we actively do for them –we are to attend to their needs, escort them, etc. The current mitzvah, the obligation to defer to them, refers to things we don’t do. For example, we’re not to contradict our parents or to sit in their special designated places.
It’s interesting to note that Mitzvah #33 says “honor your father and mother,” putting the father first, while our verse here says that everyone is to “revere his mother and his father,” placing the mother first. The Talmud in Kiddushin (30b) explains that this is because a person naturally tends to give his mother more honor and his father more deference. In each mitzvah, the Torah stresses the parent more likely to be overlooked in order to “level the playing field.”
Our verse begins by telling us to defer to our parents but it ends with “and you must observe My Sabbaths.” The meaning is clear: even though our parents “outrank” us and we must defer to them, God is the “Commander in Chief” to Whom we all must defer. Our parents do not have the ability to countermand God’s orders. If they tell us to violate Shabbos (or any other mitzvah), we must politely decline. (See Talmud Baba Metzia 32a.)
This mitzvah applies to both men and women in all times and in all places. In the Talmud, it is discussed in Kiddushin (30b-32a), Baba Metzia (32a) and Yevamos (5b-6a). It is codified in the Shulchan Aruch in Yoreh De’ah 240. It is #211 of the 248 positive mitzvos in the Rambam’s Sefer HaMitzvos and #42 of the 77 positive mitzvos that can be fulfilled today as listed in the Chofetz Chaim’s Sefer HaMitzvos HaKatzar.