How does SVD work?

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Trying to find information, and, no-one seems to know the answers.

I have a time-series, represented by $T = [0, 1, 1, 0, \ldots, n]$ the time series is then transformed into the Spectral results:

$$ S = \begin{bmatrix} 1&0 \\ 0&1 \\ 1&1 \\ 0&2 \\ 1&1 \end{bmatrix} $$

I then compute the SVD which gives me three resulting matrices u, s, v

I understand that s contains the magnitudes that relate to the columns in both u and v but, how does this work for finding the most significant data within a given series?