Data modeling is a way to structure and organize data so it can be used easily by databases. Unstructured data can be found in word processing documents, email messages, audio or video files, and design programs. Data modeling doesn't want these "ugly" data; rather, it wants data that is all made up in a nice, neat package for processing by a database.
Data modeling is routinely used in conjunction with a database management system. Data that has been modeled and made ready for this system can be identified in various ways, such as according to what they represent or how they relate to other data. The idea is to make data as presentable as possible, so analysis and integration can be done with as little effort as necessary.
We can also think of data modeling as instructions for building a database. Concentrate on the word model, and you'll get what we're going after here. To make a "pretty" database, you will want to follow a model as a means toward your desired end.
For example, if you want to analyze how many people in a given congressional district voted in the last election, you will naturally want to include a column for which party each person voted for. That kind of analysis will be valuable to members of all political parties, and it is the kind of detail that you can build into the database from the ground up, instructing the database management system to include that column of information in the resulting database. If you wanted to analyze that information specifically but didn't include a column for it in your database, you'd spend lots of time collating the data — effort that would not be necessary if you had followed the data model in the first place. Data modeling is therefore a very important skill to implement when building databases.