Explaning what a "sign of the covenant" is can be difficult and confusing. After a storm in Dallas, I saw a rainbow and began to think about the similarity of the rainbow as a sign along with circumcision and baptism. The similarities may help us understand what a sign is.
The Rainbow: In Genesis 9, God makes a covenant with Noah. God promises never to destroy the earth by water again, and gives Noah a sign. This sign points to God' promises, (Gen 9:14-16) not anything in Noah. The purpose of the sing for Noah is as a reminder of God's promises.
Circumcision: In Genesis 17, after God has promised many things to Abraham. To assure Abraham of His promises, God gives him the sign of circumcision. Paul tells us that circumcision is a "sign of the righteousness that comes by faith" (Rom 4:11). The sign is not of what Abraham does, but of God's righteousness to keep his word and promises to Abraham. Not Abraham's righteousness, for "the Lord is our righeousness" (Jer 23:6). Not Abraham's faith, but the righteousness that comes by means of faith.
Baptism: The image of Baptism is throughout the Bible. God promises many things to His people, including: his ingrafting into Christ (Rom 6:5; Gal 3:27), of regeneration (Tit 3:5), of remission of sins (Mar 1:4), and of his giving up unto God through Jesus Christ, to walk in newness of life (Rom 6:3, Rom 6:4). Like circumcision, baptism points to the promises of God, a righteousness that comes by faith, it does not point to faith but the righteousness.
What do these three signs together tell us of signs in God's covenant? The Rainbow points to the promises of God. Circumcision points to the promises of God. Baptism points to the promises of God. So the next time we reflect on our baptism, see the baptism of another, or think of what to say to someone about their baptism, let us remember that baptism is not about the person or what they can or did or do, but about God, what He did in Christ for them and does by the Spirit in them and the promises He makes to the believer, promises of His righteousness to be received by faith.