I remember a story in which a student asked Saotome sensei for some "hard training." Saotome sensei looked at him and told him to stand on one leg for an hour.
Any way, for me, "hard" training can mean a variety of different things including a physically brutal and/or vigorous training and a mentally strenuous training.
At least for me, physically "hard" training can mean anything from training with people who are better than I am who can throw me five inches under the mat to an aerobically vigorous workout consisting of a heck of a lot of ukemi. It can also be those classes in which we work on the simplest but subtlest aspects of things like movement, kuzushi, and musubi.
A mentally "hard" training may be one in which I try to maintain a mental connnection with my partner(s) all the way throughout the entire class and training with a lot of concentration. A lot of weapons training falls into this category as it's usually not very physically difficult but more mentally challenging.
I think that the notion of "hard" training is different for different people and very well will be different for the same person at different times. Whatever training that pushes people's boundaries, beliefs, and abilities is, I think, my definition of "hard" training...