Generally, the terms "hard" and "soft" are used to describe how individual dogs respond to discipline.  It should not be confused with how dominant/submissive a dog is or how aggressive it is since these are completely different traits.

A "hard" dog will bounce back easy from discipline and may also need more motivational discipline in order to get a behavior change from.

A "soft" dog will respond to "softer" discipline and may not bounce back as well to a correction especially if it is overdone.

There are pros and cons to each type of dog depending on preference.  A hard dog may be more difficult to motivate with discipline but there will be less side effects if someone is sloppy.  A soft dog will respond easier to discipline, but you will have more side effects if the trainer is sloppy in any aspect.  In some ways, if all else is equal the soft dog can be more challenging to the new trainer than the hard dog.   So "hard" dogs are not necessarily harder to train.

Here are some examples:

• You can have a soft dog that is very dominant and aggressive.  This dog may react by biting the handler easier than a hard dog of equal temperament for a relatively light physical correction that the dog feels is unjustified.  If the dog was hard he may have simply not responded to the correction.
• In the world of protection or police dogs a hard dog isn't necessary better or worse than a soft dog if all else is equal in temperament.  It just produces two different types of reactions from combat with a bad guy.  A hard dog may not care much about being beat on by a bad guy which has obvious benefits for a dog that may need to stay in-gauged,  but this dog is also more likely to get injured by not adjusting to strikes or even stabs.  A soft dog will be more reactive to being struck and is more likely to adjust in the form of moving out of the way of something striking him or transfer a bite in a way that addresses the issue.  The con of this can be during police work where a dog may need to hold a single bite while other officers rush in to assist with an apprehension. This also is not good for most sport training where a dog is expected to keep a single calm bite on an agitator while enduring a couple stick hits.

Notice that hard and soft have nothing to do with a dog's willingness to show aggression or fight with a person or dog.  Also, a dog may be "hard" or "soft" to different types of discipline.  Therefor, a dog may be hard to leash corrections, but soft to ecollar corrections.  Or, a dog may be hard to ecollar corrections, but soft to verbal reprimands.  Hard and soft, like all temperament traits are hard to measure and generally used in relative terms.  Dog "A" is softer then dog "B", or dog "A" is soft for a German Shepherd.

Here is an example of a dog that would be considered very very hard when it comes to leash corrections on a martingale:

I personally would use a type of correction that was more motivational with less force if I was training a dog that hard.  Here is a dog of equal "hardness" but using a more motivational training tool (ecollar) in order to use less brutal force.