A data structure is a particular way of organizing data in a computer so that it can be used effectively. Wikipedia states it as:
In computer science, a data structure is a data organization, management, and storage format that enables efficient access and modification. More precisely, a data structure is a collection of data values, the relationships among them, and the functions or operations that can be applied to the data.
A data frame is a two-dimensional data structure, i.e., data is aligned in a tabular fashion in rows and columns. A data frame is a special case of a two-dimensional array, where the rows and columns are identified with labels rather than simple integer indices. This makes it easier to manipulate and analyze the data from a human perspective.