The quick answer is that traffic signals are installed when "an engineering study indicates that installing a traffic control signal will improve the overall safety and/or operation of the intersection."  In other words, when volumes and congestion get high enough, or when the number of correctable crashes exceeds a certain amount, a traffic signal will improve safety and operations.  

Many local agencies monitor unsignalized intersections on an annual basis, keeping track of traffic volumes and collisions.  They keep a list of intersections in order of the need for traffic signal installations.  In general, the intersections with the highest volumes and biggest number of correctable collisions are at the top of the list.  Depending on the agency's budget and the rate of population growth, many agencies set aside funds to install one or more new traffic signals each year.  

The volumes and collision records are compared to a list of Traffic Signal Warrant criteria.  If one or more criterion are satisfied, the traffic signal is said to be warranted.  This means the traffic signal installation would result in a net benefit to traffic operations or safety.  

For example, there are Volume criteria for the highest hourly volume of the day, the highest four hours, eight hours, or daily volume.  For each time period considered, the criterion gives minimum volumes for the major street and minor street, and the counted volumes must be equal to or greater than the minimums.  

 The collision history warrant requires that at least 5 correctable collisions occurred in a 12-month period.  "Correctable" collisions are typically broadside collisions, which are more likely to occur at Stop controlled or uncontrolled intersections than signalized intersections.  

It is important to note that because a signal is warranted the agency is not required to install one.  Similarly, sometimes traffic signals get installed before warrant criteria are met.  This often occurs in new development areas, for example, when it is reasonable to expect volumes to meet the criteria in the near future.  

For detailed information, see Section 4C in http://www.dot.ca.gov/hq/traffops/signtech/mutcdsupp/pdf/camutcd/CAMUTCD-Part4.pdf