This mitzvah seems pretty straightforward except for the fact that we already know not to perform certain categories of labor on Shabbos and lighting a fire is among them. So what does this verse come to add? The Talmud in Yevamos (6b) extrapolates that capital punishments are not to be carried out on Shabbos. (There’s a whole discussion there of things that supersede Shabbos and an explanation of the rationale that capital punishment might be one of them if not for this verse.) The Mechilta explains that this prohibition holds true not just for burning but for all kinds of execution and other penalties carried out by beis din.
The Talmud in Shabbos (70a) further derives from this verse that each category of labor is individually liable on Shabbos. If someone forgot it was Shabbos and did many kinds of labor before he remembered, he would be liable for each one independently, not just once for “violating Shabbos.”
The reason for this mitzvah is that, even though capital punishment may occasionally be necessary, nobody likes having to do it. On the other hand, Shabbos is tremendously important. Accordingly, God wants us to honor Shabbos by allowing even the condemned to rest on that day prior to meeting their inevitable fates.
This mitzvah applies to the courts at a time when capital punishments are in effect. It is discussed in the Talmudic tractates of Yevamos (6b) and Sanhedrin (35a-b). It is codified in the Shulchan Aruch in Orach Chaim 339 and is #322 of the 365 negative mitzvos in the Rambam’s Sefer HaMitzvos.
This is the only mitzvah in parshas Vayakhel and there are no mitzvos in parshas Pekudei. That makes this the last mitzvah in Sefer Shemos, the Book of Exodus. (For those who were counting, that means that there were three mitzvos in Sefer Bereishis and 111 in Sefer Shemos.)