As was pointed out, this is a very common question of inquirers so you can probably find a lot of good responses to this question on this forum and elsewhere. I will just point out a few things. When Protestants hear "save us!" they usually have only one definition in mind for "save", that is to grant eternal salvation which was the purpose of Christ's Incarnation, Death, Resurrection, and the sending down of the Holy Spirit at Pentecost. This is not the only meaning of the word "save", however, nor is it the only meaning used in the Scriptures. For instance, in Matthew 8:24-25, when the disciples were in the boat and and a violent storm arose while the Lord slept, they cried out to the Lord, "Lord, save us: we perish". They were not saying, "deliver us from the consequences of sin, from the Evil One, and from Hell", but rather keep them safe, protect them from the storm, etc.
According to the Greek Lexicon, the word "save", which is transliterated as "sozo", has as one of its meanings, "to save, keep safe and sound, to rescue from danger or destruction one (from injury or peril)", which is also a definition of the word "save" in the English language. The same word can be used to refer to being delivered from the consequences of sin and death. Now, we Orthodox Christians who pray "Most Holy Theotokos, save us!" have already been baptized and cleansed of our ancestral sin and of those sins we accumulated prior to baptism. We have already committed our life to Christ as Saviour and God. However, we understand that salvation is not a one-time decision, but the healing of our souls from the sickness of sinful passions as we struggle to live a life of obedience to Christ. If you have studied the subject of "salvation" in Orthodox teaching, and the Scriptural basis of the Orthodox teaching on this subject, you understand that after baptism a person can still be condemned if they fail to live a life of repentance in obedience to Christ and instead give serve the passions and the will of the Devil.
In our spiritual struggle to save our souls by keeping the commandments of Christ and fleeing from the snares of the Evil One, we need great help. So, we receive the mysteries, we ask God to help us, and we also ask the saints and the Theotokos to help us. The longer one is in the Church, the more one appreciates and comes to love the Theotokos, understanding the great power of her prayers to the Lord, her great purity and holiness, and also her great love for man. We cry, "Most Holy Theotokos, save us!" because we are asking for her help as we face the many trials of life which seek to divert us from following her Son, which is Christ our God.
So, the Theotokos does not grant salvation or anything else apart from Christ. The saints and the Theotokos were not able to accomplish anything apart from Christ in their life, nor can they help us now apart from Christ. The only glory that the saints and the Theotokos have is due to their obedience to Christ and His glorification of them. But those who are of Christ, who are part of His body, who have been cleansed by Him of their sins and are on the path of salvation, we receive great help in trials by asking the Theotokos to save us from the snares of the Devil by her holy prayers.
