Jesus tells the believers at Sardis that there were a few people who had kept themselves free from the general contamination. Simply put, God has always had a remnant throughout scripture - the biblical principle of a remnant existing throughout all of Christian church history as well, "which have not defiled their garments." Because they have not become corrupt, "they shall walk with Me in white." White is the emblem of innocence, and apparently is a reality in heaven. "For they are worthy" meaning deserving, proven, qualified for reward. It is only Christ in us (through faith on His shed blood) that allows us to stand sinless before God. Central to a willingness to let Jesus reign (by the Spirit) must be the characteristics of genuine love, true humility, and choosing to not live lives of flesh and lust.
Now the letter to Philadelphia, a city only 25 miles from Sardis. Here Jesus seems to be reassuring them that they were the heirs to salvation. Whoever looks to Him can walk through the door Christ has opened and "no one can shut it." Christ is the only one who can grant access to God, and Christ has given the Christians at Philadelphia access to God and no one can deprive them of it. Bottom line - Christ is saying that He has the key of David. As a material King David's key opened the door to any who would enter the Nation of Israel. Far more importantly, Jesus now and forever after opens the door for the church or body of believers - which allows all through Him to enter into the presence of God. He IS the door to the kingdom and therefore the only way to salvation.
Those people who claimed to be Jews (but were not, but were actually liars from the synagogue of Satan) were the ones who persecuted the Saints at Philadelphia. He tells them that these persecutors would eventually bow down before the believers (because He will make them) and they will know that Jesus was always on their side. Here Revelation underscores the notion that the Jews are no longer the people of God as a national or ethnic entity, since they have rejected their Messiah.