We are not allowed to add to the laws of the Torah. By that, we mean that one may not present non-Torah laws as if they are Torah laws. For example, we may not say that chicken and milk are forbidden to be eaten together by the Torah when it is actually a rabbinic prohibition. Such misrepresentation is dishonest and leads to trouble.
A perfect example of this mitzvah is found in the Midrash, cited by Rashi on Genesis 3:3-4. God had commanded Adam not to eat from the Tree of Knowledge. Adam told Chava (Eve) not even to touch the tree, but he neglected to tell her that this was his safeguard, not an inherent part of God’s command. When Chava touched the tree with impunity, she assumed the entire command was without teeth, not just Adam’s addendum. Of course, this error had disastrous results for mankind. Adding a safeguard to God’s law was okay for Adam to do – it was actually a good idea! The flaw in his judgment was in not telling Chava what was a Biblical law and what was his “rabbinic” enactment.
Some authorities limit the application of this mitzvah to positive mitzvos. For example, one may not say, “If shaking one lulav on Succos is good, two would be better!” or put five chambers in his tefillin instead of four, etc. The Torah has given us the numbers of things in these mitzvos and we may not add onto them. This also prohibits us from trying to fulfill time-sensitive mitzvos at improper times, such as blowing a shofar (with the intention to fulfill the mitzvah) on a day other than Rosh Hashana.
Some people mistakenly think that this verse somehow bans the establishment of rabbinic laws but such is obviously not the case. There are actually verses in the Torah that take for granted that there will be rabbinic laws, such as Deuteronomy 17:11, which obligates us to observe such enactment.
The reason for this mitzvah is that God is perfect and He gave us the Torah, which is His perfect Book. While we might make safeguards to keep people far from sin, we do not edit the Book itself. To have sixteen strings on one’s tzitzis rather than eight, or to sit in a succah for 10 days, is tantamount to editing the Book that tells us what we should do.
This mitzvah applies in all times and places. It is discussed in the Talmud in tractate Sanhedrin (88b-89a) and Rosh Hashana (28b). It is codified in the Shulchan Aruch in Orach Chaim 128. This mitzvah is #313 of the 365 negative mitzvos in the Rambam’s Sefer HaMitzvos and #159 of the 194 mitzvos that can be observed today as listed in the Sefer HaMitzvos HaKatzar of the Chofetz Chaim.