Offering by fire is one of the methods of offering sacrifices, referring to burning the offering with fire. {{:Old Testament Sacrificial Methods}}
Leviticus 1:9Its entrails and legs he shall wash with water, and the priest shall burn all of it on the altar as a burnt offering, an offering by fire, a pleasing aroma to the Lord.
Leviticus 2:2He shall bring it to Aaron's sons the priests, and the priest shall take from it a handful of the fine flour and oil, with all of its frankincense, and burn this as its memorial portion on the altar, an offering by fire, a pleasing aroma to the Lord.
Almost all sacrifices were fundamentally offered as offerings by fire.