The words “to offer something” are used to talk about giving or presenting something to someone. The offering is what is given. In the Bible, the words “offer” and “offering” are used to talk about someone giving a sacrifice to God (see: Psalm 4:5). There are many kinds of offerings such as the burnt offerings, drink offerings, and sin offerings (see: Exodus 40:29; Numbers 28:7; 29:11).
Paul used the word “offering” to write about himself giving his life to God to honor him (see: Philippians 2:17; 2 Timothy 4:6). Paul also wrote to Christians that they needed to offer their bodies as sacrifices to God (see: Romans 12:1). He wrote this to write about Christians using their entire bodies to honor God.