Dependency is the Procedural mechanism in TouchDesigner, where if one piece of data changes, it automatically causes other operators and expressions to re-Cook. This assures all data is consistent in a TouchDesigner process, and causes all the output displays, UIs, devices and protocols to update in realtime.
If there is a change in an operator's output data or parameter value, it causes other operators downstream from it to cook. Downstream means operators that are connected to the output of a changed node, and operators (or their parameters) that refer to the changed operator (often visible as the dashed-lines in a network).
Python Data Dependency
Because Python does not inherently have a procedural mechanism, Dependency Objects in TouchDesigner allow python data to cause downstream cooking when that data is changed.