When you create a data source, the fields are split between Dimensions and Measures. The Measure is what you want to analyze, and the Dimension is the angle of analysis.
By default, numbers are Measures, and the other data types (Text, Date, Geographical Role) are Dimensions, but that's not always the case. Any data type can be either a Dimension or a Measure.
A Dimension contains qualitative information. It always splits the Marks and is never aggregated.
A Measure is, by default, aggregated, contains quantitative information, and is almost always numeric.
Note
You can easily see whether a field is aggregated or not by looking at its corresponding pill when you use it in a shelf. If it is aggregated, the name of the field is in brackets, with the name of the aggregation at the beginning (for example, SUM(Profit)).
As you can see, it's hard to give an exact rule to discern Measure and Dimension. It's more a concept to understand and a useful way to arrange the fields. Yes...