W/L Ratio of a MOSFET
The K constant you refer to (more specifically \$K_n\$) is called the conduction parameter of the n-channel device.

\$K_n\$ is given by:

$$K_n = \frac{k_n&#39;}{2}\cdot\frac{W}{L}$$

Where

$$k_n&#39; = \mu_nC_{ox}$$

\$\mu_n\$ is the mobility of the electrons in the inversion layer and \$C_{ox}\$ is the oxide capacitance per unit area. According to Neamen the \$k_n&#39;\$ parameter is called the "process conduction parameter" and is considered to be a constant for a fabrication technology. Therefore the ratio \$\frac{W}{L}\$ is the transistor design variable.

Neamen goes on to say that the design variable is used to design MOSFETS to produce specific current-voltage characteristics in MOSFET circuits.

EDIT:

Yes w refers to width and L to length. It relates to the geometry of the semiconductor.