How does bi-wiring work?

Not very well. 

If biwiring helps, then your original speaker cables were inadequate. 

"Bi-wiring" is not a marketing ploy.  But may not be the best way to get the most bang for the buck for some listeners.  All things being equal, if you break out the total gauge of one cable into 2 cables, you'll be adding manufacturing costs in producing 2 cables, complete with another outer jacket, terminations, and additional labor. 

Part of the cost/performance bi-wire "argument" is that the higher frequencies do not require as much gauge as the lower end.  Therefore, put less of the "good stuff" (i.e. better material) on the top end thus extracting the best sonics from those materials, and bulk up (add meat) to the bottom end with less expensive materials to get more gauge.  This optimizes the cable budget using the most cost effective materials where they'll yield the best sonic benefit(s).

Some are not fans of additional jumpers and connections with a single cable/biwire connections, and prefer the straight line from the amplifier to the speaker input terminals that bi-wiring provides.

We can argue this until we figure out how to plug a digital bitstream directly into our brains.  I think it's a cost/performance conversation with no "winners" or "losers" in sonic performance if it's done "right."

Simple. It doesn't. I suppose in the instance where someone is using 24 gauge wire it might help, but using one 18 gauge wire would do exactly the same thing. This is a great example of lay intuition. The industry is perfectly willing to support it because they get to sell you another stupidly expensive cable. 

Now, bi amping is another issue. This is where you delete the passive, analog crossover entirely and use an electronic analog or digital crossover and separate amps to drive each driver. This can have huge advantages if done correctly. It requires careful amp selection and crossover programming. 

Some people believe the base gives feedback in to the highs this why some designers bi wire the proper way. One set for base one for highs