If I understand correctly:
"Ik begrijp het concept niet" = I do not understand the concept (general statement), while
"Ik begrijp niet het concept" = I do not understand the concept (but I understand other ones. It specifies that it is that concept in particular that I don't understand.).
Is this correct?
As for the translation of the second sentence, it would be 'Ik begrijp dit concept niet.' (I do not understand this concept)
The second one cannot be used. Well, it can be used but only if you are making a list.
Ik begrijp niet: het concept, etc.. (Though even this I would not advise)