If in t-SNE digaram of binary classification both classes follow the similar curve what does t-SNE diagram show?
To have the intuition, let's make simplify the problem. Let's say that you are using PCA and that you are getting a linear function.

If you don´t get any cluster it means that it is not possible to separate them by linear combinations of the features that you have. And since it is a linear function, as you move in this direction there is a change in the variance. 

t-SNE is similar to PCA but it does non linear combinatios of features. And the dimensionality reduction that you have mantains the variance in a non linear way. 
So just change the world linear for non-linear in the second paragraph to answer your question.

By the way, this doesn't mean that if you make a classification problem with Machine Learning you are going to have bad results. ML can still work in this case.