An MR scanner measures a picture's spatial frequencies, not the picture. Erase, undersample and spoil the frequencies here and watch what happens to the image. Drop in a picture of your own if you like; it stays in your browser.
Every point in k-space is one striped wave; the picture is all of them added up. The middle holds the slow waves, which carry contrast and the broad shapes. The edges hold the fast ones, which carry fine detail and sharp edges. Use One wave and click around to see the stripes each point stands for: further from the centre, finer stripes.
Across is the frequency-encode direction, up and down is phase encode, read one line at a time. That's why skipping lines folds the picture over on itself vertically (aliasing, which parallel imaging undoes), why motion between lines leaves ghosts along that direction, and why a single bad data point, a spike, lays stripes over the whole image. Cutting k-space off sharply leaves rings at edges (Gibbs ringing); keeping just over half and filling the rest with zeros is partial Fourier.