Fluency is an important aspect of learning a skill. The really casual way of defining fluency would be to say that you “know how to do [the skill]”. Consider a kid who just tied his shoe for the first time with a lot of guidance and prompting. And think about how that’s different from when most people tie shoes and don’t even think about their actions. Shoe tying is fluent.
When a new skill is learned, it’s not fluent at first. It takes practice and repetition for a skill to become fluent. But sometimes, especially if there is poor instruction or too much prompting from an instructor, the learner may not become fluent. 
When I’m teaching, I try to give the students a lot of time to practice a skill. I want to see it happen again and again and again. I give them feedback and then watch some more. In many training classes, the instructor will have a team do a skill just a few times, often with a lot of prompting. That can give the dog owner and the instructor a false sense of the true skill level. If the person isn’t able to do the skill without the prompts, how are they going to be able to practice at home?
This often means breaking the skills into very small parts, sometimes smaller than what is needed for training the dog. The handler needs to be able to focus on learning just one skill at a time. It takes more time upfront, but when students are able to practice successfully at home and have a strong foundation skill set, later training is able to progress faster than if we didn’t have a few fluent skills.
Next time you’re in a class or are watching a training class, consider:
- How fluent are the human students?
- Can they perform the tasks without constant instructor prompting?
- Do they have sufficient time to practice with the instructor watching and giving feedback?
- Has the person reached a fairly high fluency level before the task is made harder?
- How is the instructor monitoring fluency?