Measure:
Measure is a "Calculated Field" in Power BI DAX.
Example: Total Sales, Total Salaries, Average Quantity and so on.
To create a calculated field, you must use the data which is Fact. Because the data which is Fact allows calculations on the data.
Fact:
Fact is numerical data which will allow calculations such as sum, avg, max and so on.
Example: Sales, Salaries, Quantity and so on.
Dimension:
Dimension is non-numerical data which will NOT allow calculations such as Name, Day, Country and so on.
Example: Name, Day, Country and so on.
To know about Power BI DAX in detail Click Here