The higher the taming effectiveness in Ark Survival Evolved the higher the level your dino will be when tamed. Higher-level dinos will be better fighters and have a higher utility than lower-level ones. Taming effectiveness is all about the number of times a dino eats while being tamed. All creatures in Ark have a hierarchy of preferred foods with some minor exceptions like the mantis. The more preferred food the fewer times the animal will eat, increasing the taming effectiveness. This usually translates into shorter taming times so it is a huge benefit to have the preferred food of a particular species.
I always use dodoex for my taming calculator. Certain events in Ark can shorten taming times, and reduce the amount of food in the calculator, but it is a great place to learn the minimum time, and a dino's preferred food hierarchy.
The last thing to note about taming effectiveness is it can drastically drop, and even go to zero if the dino is hurt after it is unconscious. This could happen if you shoot it while it is falling down, or if some wild dino thinks it looks like a tasty snack.