Understanding the concept vanishing gradient and exploding gradient problem in terms of training data
I always refer "Andrew NG" documents if available for any ML understanding. I believe that Youtube link Vanishing and Exploding Gradient, will help you in understanding the concept in a better way.

Still a brief from my side: 


  DNN of K layers without an activation function, will be like
  multiplying K coefficients(weights) together. Somehow if you received
  initial coefficient value &lt; 0, in such a case during back
  propagation till you reach to the starting layers (from Input layer
  side), it may possible you completely lost the value of gradient,
  as gradually you are multiplying smaller value i.e. vanishing a value. Similarly if initial
  coefficient value > 0, multiplying together will form a very big
  number i.e. exploding a value.