How does the solvent determine whether mono- or tribromination of phenol occurs?
In aqueous medium, phenol is deprotonated to a certain extent, forming the phenoxide ion in which the ortho and para positions are even more activated than in phenol itself. Hence, trisubstitution occurs here.

$$\ce{PhOH + H2O &lt;&lt;=&gt; PhO- + H3O+}$$

In an organic solvent, phenol is not deprotonated and monosubstitution tends to occur. 

ron also pointed out in a comment that: 


  
  The concentration of $\ce{Br^+}$ is higher in water than in $\ce{CCl4}$ making the reaction faster in water.
  The dielectric constant of water is much greater than that of $\ce{CCl4}$, so the former solvent will better stabilize the charged intermediate, again accelerating the reaction.