The leash is the #1 tool of dog training and dog ownership. The leash is so much more than what most people use it for (have their dog drag them down the road on their morning walks). The leash is a means of communication, a safety tool, and training wheels for more advanced forms of obedience.
We can use the leash in several different techniques to convey different messages to our dogs about what they are doing, if we like what they are doing, if we don't like what they are doing, and guiding them to what they should be doing. Combined with lots of body language and rewarding, leash handling is the best way to communicate what we want from our dogs!
If I'm taking my dog for a walk, and they suddenly see an animal that decide they really want to chase, the leash is the best tool we have to prevent our dog from running across traffic to chase a squirrel. My dog is off-leash trained, she is extremely obedient and proofed against some pretty intense distractions, but if its that 1 in hundred times that she decides she's gunna get the zoomies in the middle of a training session, I would never forgive myself if something horrible happened that could have been prevented with a simple leash.
Off Leash Training is Learned On Leash... what this means is that you can always train as if your dog is off-leash while still being on leash. Especially earlier in training, the worst thing you can do is to take the leash off too early.
First of all, all fifty states have some form of leash laws, so regardless of how well trained your dog is, (or you think they may be) walking your dog on public property or around your neighborhood, or on those trails off-leash is illegal. That being said, if your dog doesn't bother anyone and has a solid heel and recall command, then probably no one is going to bother you.
The leash law information is extremely important because there are law abiding citizens out there, like myself, who do enjoy walking their very highly dog aggressive dog ON LEASH! Why is this important. Let's say you've decided to take your dog for an off-leash stroll, but your dog's recall isn't as good as you think it is. Now your dog is making a "bee-line" for my dog, and I'm yelling at you to call your dog because my dog is about to eat your dog.
I SHIT YOU NOT...
This literally happened to my husband and I while we walked our dogs, on leashes around my neighborhood. My 100+lbs german shepherd, is dog aggressive, and people aggressive! All of a sudden another fairly large german shepherd is barrelling towards us off leash. My dog is ready to murder this dog running at us, with its family strolling about 100ft behind him. As I yell "Call your dog!" and they repeated tell the dog to come over and over(uselessly).... they send their child to come and gather the dog who is now trying to fight my dog. This kid could not have been more than 8 or 9 years old and I was pretty sure my dog weighed more than him... Oh yeah, and my dog hates kids.
Point of the story: Don't be that guy.
Oh yeah, off leash training. Once you are 99% comfortable walking your dog with a 100% loose leash at all times, and have them come when called 99 out of every 100 times (they aren't perfect), then you can start practicing off-leash. Even then, I would recommend to start in an enclosed area first, and work up to low distraction, less populated areas where you are unlikely to run into the other people or dogs. Then practice around familiar dogs, and toys, and food, and any distraction you can think of!