The flour offering was called the korban mincha, the same name by which we call the daily afternoon prayer service. The word mincha literally means a gift and the korban mincha was an offering that was brought voluntarily.
A korban mincha was brought from fine flour, with olive oil and frankincense. The kohein would scoop up three fingers’ worth in a process called kemitzah; this flour was then burned. The rest was then given to the kohanim. A flour offering could also be baked, cooked or fried into loaves or wafers.
A sacrifice of flour may not be as emotionally compelling as a sacrifice brought from animals, but it was still a gift to God, given freely, and served the purpose of drawing people closer to Him. There were other types of meal offerings, as well. These included the 12 weekly loaves of show bread (see Mitzvah #97), two loaves brought on Shavuos (which we’ll come to in Mitzvah #307), the mincha brought by the Sotah (which we’ll get to in Mitzvos #365-367), and the mincha brought as a variable offering by someone who couldn’t afford animals or birds (see Mitzvah #123), among others.
Most mincha offerings were of fine wheat flour (as stated above) but some, such as the Sotah’s offering or the Omer (brought on Passover), were of barley. Most were largely eaten by the kohanim, but some were burnt in their entirety. As per verse 2:11, the meal offerings could not contain leaven, as leavening agents were not permitted to be burnt on the altar. (The two Shavuos loaves were leavened but those were not offered on the altar. Nevertheless, Leviticus 23:16 calls that a mincha as well.)
The obligation to properly offer the korban mincha applied to male kohanim when the Temple was standing. It is the topic of the Talmudic tractate of Menachos (“menachos” being the plural of “mincha”). It is codified in the Mishneh Torah in chapter 13 of Hilchos Maaseh HaKarbonos and is #67 of the 248 positive mitzvos in the Rambam’s Sefer HaMitzvos.