Bey resonance in a nutshell, with a few major spoilers about Cho-Z/Turbo:
When a Blader is effectively able to control their Bey's movements (i.e. calling out and achieving a Special Move) they have some resonance with their Bey. When a Blader is spiritually connected to their Bey (i.e. being able to talk with and understand its avatar) they have a lot of resonance. Resonance increases the Bey's power through emotions. When the Blader displays their true emotions in a battle, their Bey feels that emotion, giving it a boost in power. Valt's love for intense battles leads him to pour his heart out in battle, which is the emotion that Valkyrie responds the most to. Shu's determination to not hold back leads him to having a clear and concentrated mind, which is what fuels his Spriggan's power. As Red Eye, anger fueled Legend Spriggan and Spriggan Requiem because they were made with the sole intention of gaining power. Free's torment is what lead him to unlocking Nothing Break, since he never took battles seriously before facing off against Lui. Aiga, being new to Beyblade at the beginning of Cho-Z, was focused on becoming strong with his partner, which is why he and Achilles talked to each other. When Aiga started caring too much about winning and less about fun, he made sure to not hold back, which is why he gained the purple aura that symbolized dark resonance and, in turn, broke Vise Leopard and Winning Valkyrie. When Achilles broke, Aiga realized that he had taken things too far, so he decided to care more about Achilles again. He still wanted to get stronger, but not just for personal gain. He wanted to become like Valt, which meant that he had to grow alongside his Bey instead of pushing Achilles too far past its limits. This reignited the original resonance that Aiga had when he first made Z Achilles, which is what ultimately allowed him to get revenge on Phi for breaking Z Achilles and achieve his goal of beating his idol, Valt Aoi.