An object data model is a data model that treats data sets as "objects" by assigning properties and values to them, and otherwise structuring data to be more malleable and versatile than a simple list of data points.
Object data models developed as alternatives to simple linear data models. If you have a list of items, it is easy to store them in a spreadsheet, but not as easy to cull data to form big-picture perspectives. Object data models help to fulfill bigger goals around big data and analytics.
An object data model is that data or code is composed of modules that combine data and procedures that work on the data. With this type of model, data handlers can ask advanced sets of questions about sets of data, such as: how many of these "objects" conform to a certain format, and how much data do each of them hold?
This idea is also useful in object-oriented programming, which brings the object model to code.
As systems deal with larger and larger sets of information, object data models are helping by making data sets more responsive to queries and other types of analysis.