NOTE: I am slightly adjusting the wording of the answer to this question by removing the word "seals," which has not historically been used by Baptists in reference to the ordinances.
Question 43: What are the sacraments or ordinances?
Answer: The sacraments or ordinances given by God and instituted by Christ, namely baptism and the Lord's Supper, are visible signs that we are bound together as a community of faith by his death and resurrection. By our use of them the Holy Spirit more fully declares the promises of the gospel to us.
How did we arrive at the conclusion that there are two ordinances and that they are baptism and the Lord's Supper? Not all Christians have agreed on this point. Although the definitive list of seven sacraments was not finalized by the Catholic Church until the late Middle Ages, for centuries Roman Catholics have held that there are indeed seven: baptism, confirmation, the Eucharist, penance, marriage, ordination, and anointing the sick.
Protestants have disagreed with this claim, arguing that in order to qualify as an ordinance/sacrament, a practice must be instituted directly by Jesus to be observed by his followers as a visible representation of the gospel until his return. Only baptism and the Lord's Supper fit this criterion.
In both cases, Jesus did not begin new practices out of nowhere but rather instituted new forms of existing practices. Prior to Jesus' ministry, John the Baptist administered a baptism of repentance to prepare Israel for the coming of the Messiah (Mark 1:1-8). Jesus' ministry continued that same practice, even though Jesus himself did not baptize personally but entrusted the task to his disciples (John 3:22-26; 4:1-2). After his resurrection, Jesus explicitly commanded his disciples to make disciples of all nations, a task that included baptizing them in the name of the Father, and of the Son, and of the Holy Spirit (Matt. 28:19). The addition of the triune name to the practice of baptism signified that baptism is now the public entrance into the new covenant, where we are united with the triune God who has been revealed as such through the completed mission of the Son and the gift of the Holy Spirit, both sent by the Father in heaven.
As for the Lord's Supper, Jesus instituted it with his disciples in the context of a Passover meal, a practice inherited from the book of Exodus (Luke 22:7-23). In Paul's recounting of the event, the use of the phrase "as often" in 1 Corinthians 11:25-26 indicates that Jesus gave the Lord's Supper, not only to his disciples on that one occasion, but with the intention that it would be an ongoing practice, as indeed it was for the early church and has been for 2,000 years.
Some (non-Catholic) Christian groups have argued that the practice of footwashing should also be considered an ordinance because it fits the same criterion as the other two practices. However, most Protestants have rejected this conclusion based on the argument that Jesus' intention in John 13:14 is not to establish a new ceremonial practice but to command his followers to love one another and to demonstrate that love through humble acts of service to one another. We who live in a society in which our feet are covered most of the time, and in which we are not often walking on dusty roads, do not normally need our feet washed by others. But we do have other needs, and we fulfill Jesus' command when we move to meet those needs for each other as we have opportunity.
Christ instituted two practices to picture the gospel during the time between his two comings: baptism and the Lord's Supper. That explains why we recognize only two ordinances.
Suggested passage for personal or family reading: Romans 6:1-4. How does baptism picture the gospel? If you have been baptized, how should that affect the way you live?