When answering this question it is helpful to attempt to define our terms. Briefly, the term Reformed must be understood historically in three ways:
First, Reformed means Calvinistic. Reformed Baptists believe that Salvation is all of grace. God is Sovereign and He has determined the end from the beginning. He has decreed all things including the salvation of particular sinners from every tongue, tribe, and nation throughout human history. He has done this not because of foreseen faith, but for His own glory. God is Sovereign but man since Genesis 3 is totally depraved; unwilling and unable to make himself acceptable to the perfectly holy God of heaven and earth. It is because of mans’ total depravity and moral inability that God has chosen, or predestined, an innumerable body of men, women, and children to be saved by grace through faith in Jesus from His wrath and curse both in this life and the one that is to come. Those elected by God for salvation have had a perfect atonement made for them by Jesus Christ. Jesus did not die for all sinners in general, but for all of the sins of a particular people given to Him in the covenant of redemption made between the Father, the Son, and the Holy Spirit before the foundation of the world. Those whom the Father has elected, and the Son has made atonement for, the Holy Spirit draws irresistibly to Jesus Christ through grace given faith in the gospel. The Spirit makes the sinner willing to believe, and to repent of sin, and to live after obedience to Christ’s commands motivated by gratitude for the grace that has been received. Those elected by the Father, atoned for by the Son, and drawn by the Spirit will absolutely persevere in the faith and receive the eternal crown of glory, not because of their ability, but by the power of grace. What God begins by grace, He brings to completion by grace.
Second, Reformed means Covenantal. God deals with sinners by means of covenants. He gave Adam a covenant of works that if he had fulfilled would have won for the human race eternal life. Adam failed, and as the representative, or federal head of humanity, all men and women descending from him by ordinary generation are fallen in him, and are by nature and practice, alienated from God, unable and unwilling to fulfill the righteous requirement of the law, and are therefore under His wrath. By sheer grace, God was pleased to enter into a covenant with His Only Begotten Son as the federal head concerning the salvation of His elect. This covenant of grace is revealed first to man in Genesis 3:15 in the promise of the singular offspring of the woman who would, in time, crush the seed of the serpent by giving His own life in the place of sinners, and is revealed by further steps through types and shadows given through the various covenants between God and men. It is only through this covenant of grace, with Christ as the Mediator and Federal Head, by which the elect are saved. All who have been saved, and who will be saved, from Adam until Christ returns on the Last Day, have been saved by virtue of grace through faith in Jesus. Although this covenant has been promised from of old, it is the New Covenant inaugurated in time through the life, death, and resurrection of Jesus Christ. All who have been saved in every age were naturally born into Adam, and supernaturally born again by grace into Jesus Christ. Covenant theology provides us with a hermeneutic by which all of the Bible is relevant to all of God’s people. God does not have two peoples with two distinct destinies: He has one people made up of redeemed sinners from every tongue, tribe, and nation who are one under Christ. There is, and has only ever been, one way of salvation: By grace, through faith, in Christ Jesus, and He has been revealed in the Scriptures alone.
Third, Reformed means Confessional. Historic Protestant Christianity is tied to the confessions written and affirmed by Christians from the 16th and 17th centuries. We can think of the robust statements of faith recorded in the Augsburg Confession, the Thirty-nine Articles, The Heidelberg Confession, The Westminster Confession of Faith, the Savoy Declaration, and the Second London Baptist Confession of Faith. Those who are Reformed believe that their Confession of Faith is the most faithful summary of the Scriptures written by uninspired men. The confessions create the boundaries of the local churches that subscribe to them. Rather than being general or ambiguous statements of the Christian faith, confessions are highly detailed and as a result create greater unity and doctrinal clarity among those churches who hold faithfully to them.
The term Baptist refers to three primary things.
First, is the belief that baptism is only rightly applied to those who demonstrate credible faith in Jesus, and repentance from sin. It is not those who are born who are the proper subjects of baptism, but those who have been born again by the regenerating work of the Holy Spirit.
Second, only those who have been rightly baptized after a credible profession of faith should be admitted into the membership of the local church. Baptists believe that the local church should, so far as it is possible to discern, be a regenerate membership.
Third, Baptists believe in the autonomy of the local church under Christ in Scripture. Baptists by definition are non-denominational. God has provided all that is necessary for the organization, governance, worship, and discipline of the local church in the all-sufficient Scriptures. Although Baptists believe that there is no outside governance over the local church, we also affirm the biblical model of formal associationalism in order to advance the gospel and to mutually support local congregations fully subscribing to a common confession of faith.
For an even longer answer download and read this PDF article: What is a Reformed Baptist Church? by Jim Savastio, Pastor of Reformed Baptist Church of Louisville