Eimurim were fats and other parts of a sacrifice that had to be burned on the altar. While speaking of the korban Pesach, God tells us not to leave these fats and innards overnight, as that would disqualify them. If they are left out overnight, they are called “nosar” (“remaining”).
The basis of this mitzvah is that the sacrifice must be performed in its proper time. It’s disrespectful to procrastinate and to put off fulfilling one’s obligations, especially to God, so the Torah cautions us not to put off until tomorrow what must be done today. One who neglects to burn the eimurim in the proper time is one who really doesn’t care about his offering and what it represents.
This mitzvah was incumbent only upon male kohanim (priests) at a time when the Temple was standing. This mitzvah is discussed in the Talmud in tractate Pesachim (59a-b) and codified in the Mishneh Torah in the first chapter of Hilchos Korban Pesach. It is #116 of the 365 negative mitzvos in the Rambam’s Sefer HaMitzvos.