Nyquist Theorem - Why unique frequencies upto Fs/2 and not Fs? f+Fs is start of Aliasing
Since you stated you are still confused, the following graphics may help further understand the other two good answers:

First be sure that you understand what the sampling process (which is multiplying an analog signal by a stream of impulses in the time domain) looks like in both time and frequency; a stream of impulses in the time domain is a stream of impulses in the frequency domain. Multiplication in the time domain is convolution in the frequency domain, so if we sample by multiplying by an impulse every T seconds, we convolve our waveform with a frequency impulse spaced every 1/T Hz:



An example of this is sampling a 3 Hz cosine (where a 3 Hz cosine is represented in the frequency domain by an impulse at + and - 3 Hz) with a sampling clock of 20 Hz as shown in the graphic below. The top spectrum represents the input (analog) spectrum of the cosine wave. The middle spectrum is the spectrum of our sampling process (an impulse every 20 Hz including DC), and the bottom spectrum is the digital spectrum resulting from convolving the previous two.



Note that the analog spectrum was replicated in this process; so everything from $-F_s/2$ to $+F_s/2$, what we call the "first Nyquist zone", is duplicated centered on every multiple of $F_s$. (Where $F_s$ is the sampling rate). Thus the unique spectrum is completely defined by what is between $-F_s/2$ to $+F_s/2$, but we could easily show instead the spectrum for 0 to $F_s$, so it is somewhat arbitrary what slice of the spectrum we choose.

Note for real signals, the negative frequency components are the complex conjugate of the positive frequency components, so in that case not unique: they are completely defined by the positive frequency components so in that case that is all we need to present to provide all relevant information (the spectrum from DC to $F_s/2$).    

That is not the case for a complex signal, as explained by hotpaw2 and shown in the graphic below.