Horizontal traceability shows relationship among related items such as between requirements itself. It traces dependent items within a development phase. Vertical traceability is a characteristic identifying the source of requirements typically from requirements to design, to the source code and to test cases.
Horizontal traceability is an aspect identifying non hierarchical similarities, mutual properties, interactions, etc. among requirements and work products. For example assume we want to implement a login function in four different types of browsers. There are four sub teams to do this. Here the functional requirement remains the same. If any change in requirement happens, then it needs to be reflected across all the four browsers. These kind of dependent requirements are easily traceable if horizontal traceability is marked among them. To make it more clear horizontal traceability is a sibling kind of relationship while vertical traceability can be treated as parent-child relationship.
Both horizontal and vertical traceability can be bidirectional. Establishing and maintaining robust vertical and horizontal requirements traceability helps to trace transmission of a change to all affected work products and customers/users. When a change in requirement happens, effective impact analysis is possible with the help a traceability matrix. Thus we are in a better position to find adverse side effects due to a modification in a work product and ensure that the change did not hinder compliance with user requirements.