Ok, let me go back and explain that. This world operates on different functions than the one you know. One of those things is until you do certain things, other shit's locked from you. Like climbing cliffs.

But things you know like moving lightning fast, you're limited to average human speeds. It's a pain. Badges unlock things. More gym leaders you take on, more you can do. Unless your trainer card said 'breeder' then they just need the hm to do whatever.

Hms are those bigger things like Strength, fly, surf, etc that you teach to pokemon which is your buddy right there. If you've got a pokemon that can fly, cuts your travel time in half or more. Any of that make sense?