Interpretation of a sampled signal in the frequency domain
First, $i$ is not the imaginary part, but the imaginary unit. This tells you that the signal, under suitable conditions, admits a discrete time Fourier transform.  Its is a linear representation of the discrete signal. It provides you with a spectral interpretation, ie a view of the content of the signal  as a linear combination of waves, pure frequencies  indexed by a continuous index $\omega$. Pure frequencies are cisoids or complex exponentials/sinusoids, by definition 

$$e^{-i2\pi\omega nT} = \cos(-2\pi\omega nT)+i\sin(-2\pi\omega nT)\,.$$

The relative importance (weight) and "timing" of these waves is given by $\tilde{Y}(\omega)$, by its magnitude and phase, respectively. Another interpretation of the sum of products is a scalar product between the signal and the different waves. If the scalar product is high, the signal looks like the pure wave  a lot, and the corresponding frequency is very "present" in the signal. If is is low, this component is not really present in the signal. The whole spectrum, made of all the $\tilde{Y}(\omega)$, tells you about the content in "each" frequency in your data.

The two links above drive you to the excellent site of J. O. Smith, and the mathematics of the discrete Fourier transform, an perfect starting point to understand these concepts.