A normal dataset (also, pivoted, wide, crosstab) organizes data in a table format so that readers can scan the data quickly and find the data that they want.
For example, the Normal image below includes data by Pet Owner and the different types of pets (Dogs, Cats, Turtles). As a human reader, you can assume that the columns Dogs, Cats, Turtles all fall under the category Type of Pet and illustrate the Number of Pets for each owner, though these column titles are not explicitly stated in the dataset.
An unpivoted dataset (also, tabular) is a flat file that a database reads as a table one row at a time. Each row includes only data about a single observation in time and place.
For example, the Unpivoted image below includes data by Pet Owner, Pet Type, and Number of Pets. In this dataset, one row contains a single observation (Amy, Dogs, 3). Each of the dimensions of the data (Pet Owner and Pet Type) are explicitly stated, as well as the measure (Number of Pets). Notice that for each type of pet, the list of pet owners repeats.