There are a few things incorrect with many of the other explanations here.
1. Many of the comments describing algorithms make it sound like algorithms always work no matter what which is untrue. Algorithms typically only move 2-4 pieces around at a time meaning you need to do moves that setup the algorithms properly. You can’t take an arbitrarily scrambled cubed and throw several algorithms at it without thinking and expect a solution.
2. Cubers don’t use algorithms for every piece. The entire first two layers are solved “intuitively” in the sense that they are truly manipulating pieces on the fly with simple movements. Algorithms don’t kick in until until solving the top layer (and occasionally one step beforehand). The magic comes from picking the two algorithms you need to do the last layer from a list of a few hundred based on what patterns you see.
3. I recommend the YouTube channel jperm as he does breakdown and analysis videos of world record solves. He recreates the scrambles and explains step by step what moves the cuber used what they were looking for to lead to the next step quickly
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