It's because the atoms are arranged in a long chain that interacts mostly with itself, and very little (at least for the electrons of interest) with atoms in other chains. A better term might be "quasi-1D" since of course the atoms themselves are 3D, but 1D does convey the key idea that the parts of interest are interacting along a single dimension of space.
Quantum mechanics does very odd things when you insist that the wavelike properties of matter be limited to lines, planes, or for that matter points (quantum does, atoms). You can see one reason by thinking about waves in tunnels: They don't dissipate! A blast deep within a tunnel has nearly the same force when it exits it does when it happens deep in the tunnel, which is why explosive trucks are banned from long tunnels.
In quantum mechanics your waves are further constrained by the need to arrive at a resonant, repeating pattern, which somewhat ironically is called a "stationary" solution since whatever it is doesn't appear to be moving when examined from our classical perspective. For long chains, that means that any long waves (e.g., conduction electrons in a metal) must stabilize into solutions that are topologically similar to ordinary skip ropes, ones that can have one, two, three, or many more loops. For a semiconductor such as CdSe you have more complicated electron configurations and energy levels, but you still maintain that need to settle into nicely resonant solutions.
That in turn can lead to really interesting electronic and optical behaviors, which is why the fields of 1D and 2D (and 0D, quantum dots) have had and continue to have a lot of interesting materials research going on in them.