Once the molds are made plastic is dirt cheap and fast to crank out via injection molding. Metal and glass parts for something like a phone are machined, which takes a lot more time in addition to the increased cost of the raw materials. Machining does have substantial advantages however: It's a bit easier to hold VERY tight tolerances which are typically an indicator of build quality. Also CNC machines can be reconfigured much more cheaply to make changes or produce a different part. The molds required for industrial scale production of plastic parts are hideously expensive until volume brings them back into line. As another commented noted, the lighter weight of plastic saves fuel and cost when shipping.
The design constraints also differ between the two processes. For example molding (at least to some extent) requires slightly angled walls to allow the part to release easily, and any undercuts require more complex/costly molds. That being said, an endless range of shapes are attainable in molded plastic far more easily than machined metal or glass parts which typically consist of more planar surfaces with chamfers/fillets. It's also possible to use FAR fewer parts if one works with plastic, which may save substantial machine time and cost. It's also much easier to do colors obviously, as an additional process (example: anodizing) isn't necessary.
So what does this mean for these two phones? The 5C may be much cheaper to produce in large volumes, which is worth noting since much has been said about this phones target Asian demographic. It may be cheaper because parts can be produced much more rapidly, the number of parts is fewer, and far less human labor is required to assemble the device.
Ironically plastic supposedly diminishes RF signals less than metal and this "cheap" iPhone may enjoy slightly better reception than it's flagship cousin.
And a wild guess: a cursory glance reveals the internals appear to be the same as the iPhone 5, which may explain why the 5 will no longer be offered: Apple has found a venue for their existing production line and potentially some stock as well.
Would love to know more if anyone else has thoughts.