How does the production of pure, crystalline silicon via the Czochralsky or Siemens process?
How does trichlorosilane $\ce{HSiCl3}$ help in the purification of silicon?

Trichlorosilane is a highly volatile compound with a boiling point of 32 °C. This means that it can be destilled off the raw material and separated from impurities.

The purified trichlorosilane can either be decomposed thermally

$$\ce{4 HSiCl3 -&gt;[\Delta] Si + 3 SiCl4 + 2 H2}$$ or reduced with hydrogen

$$\ce{HSiCl3 + H2-&gt; Si + 3 HCl}$$

This does give you rather pure silicon, but it is, at best, polycrystalline.

What's the Czochralski process good for?

Note that this in't just a melting/cooling cycle! 

The crucial point in the method is the use of a rotating, monocrystalline seeding crystal, dipped into (previously purified) molten silicon. The goal is to obtain huge, monocrystalline silicon rods of defined diameter, that can be used in the production of wafers.