The Psalms, as a poetic book, often seem to confuse people, particularly those outside the Church. For example, many atheists accuse Scripture of being the uneducated word of bronze age goat herders because Psalm 96:10 says the Earth is immovable, whereas we now know it is in continual motion, spinning on its axis and orbiting the sun.
However, when we turn to Psalm 99, we find the opposite claim. This Psalm begins by telling us that the Earth should be moved because God reigns. This is because the Psalms are not as strictly literal as other portions of Scripture. The word "Psalm" literally means "hymn". It is a collection of sacred songs, and so, much like songs in our own language, is largely metaphorical. They may contain literal truths, but it is riddled with figures of speech.
In neither Psalm 96, nor Psalm 99, does "move" literally refer to the physical motion of the planet. In the 96th Psalm, God isn't saying the Earth is a stationary rock, but that there is an unchanging way in which it will be run, and, more importantly, judged. God is as much God in Egypt as in England. In Iraq as in Israel. In Russia as in Romania. All throughout the Earth, there is a natural order that cannot be broken, and should not be rebelled against.
In the 99th Psalm, it means a "movement" of the heart. A shift on both a personal and cultural level. It means to be moved to praise and obedience. If you like, we should be "moved" in the Psalm 99 sense towards being "immovable" in the Psalm 96 sense.
If you've never studied the Bible in any reasonable depth, or even read it, you can be forgiven for making the mistake of assuming Psalm 96:10 teaches a faulty cosmology. But the sad truth is, those who told you to believe that have not been moved according to the teachings of Psalm 99:1. Rather, they are immovable in their sin. Their hearts are rebellious against God, and it seems they intend to stay that way.
But because the Earth is immovable in the true sense of Psalm 96:10, they will eventually discover the truth of Psalm 96:13: "For He is coming, for He is coming to judge the earth. He shall judge the world with righteousness, And the peoples with His truth." That time has come. 2,000 years ago, the Lord entered creation through the womb of a virgin, being born as an innocent baby boy by the name of Jesus. As He grew, He did not sin, as we do. He lived a perfect life, never turning from God to the right or the left.
Because He never sinned, Jesus never deserved punishment. Yet, He received it. He was put through a sham trial, beaten half to death, and hung from a cross by nails in His hands and feet. Jesus died, facing the full wrath of God for sin.
In effect, Jesus served the sentence we should serve. But there is a condition to this. According to Scripture, all who confess Jesus as Lord, and believe in their heart God raised Him from the dead, will be saved. But those who do not do so stand condemned in their unbelief. Thus, there is potential for all people to either be saved or condemned. Your faith determines this. On the one hand, you can be stubborn. You can reject Jesus, and use out of context quotes from the Psalms as an excuse to do so. In this case, your judgement is coming as soon as the end of your life. Alternatively, you can embrace the free gift of grace offered to you: Eternal life, paid for by the blood of Christ. Everything evil you have ever done, said, or thought, will be applied to His cross. The choice is your own.