What can we understand when we increase the $N$-point DFT for a given signal?
If the signal length $M$ remains the same but only number of points $N$ in DFT is increased (assuming $M \leq N$) then this will give you the finely spaced samples $X[k]$ of the same true spectrum $X(e^{j\omega})$ as given by the DFT frequency sampling relation: also known as the zero-padding result 
$$X[k] = X(e^{j\frac{2 \pi}{N}k}) = \sum_{n=0}^{N-1} {x[n]e^{-j\frac{2 \pi}{N}k}} = \sum_{n=0}^{M-1} {x[n]e^{-j\frac{2 \pi}{N}k}} ~~~ , ~~~~  k=0,1,2,...,N-1 $$ 

On the other hand, if both the analysed signal length $M$ and the DFT length $N$ are increased (assuming $M=N$) by using a longer analysis window (considering $x[n]$ defined for a very long, possibly infinite length duration) then the windowed true spectrum of the underlying signal whose samples are investigated, is also enhanced, thereby providing samples $X[k]$ of a higher frequency resolution spectrum of the very long length signal $x[n]$