The grand tour is a technique originally developed by Daniel Asimov 1980–85, which is used to explore multivariate statistical data by means of an animation.
This technique is like what many museum visitors do when they encounter a complicated abstract sculpture: They walk around it to view it from all directions, in order to understand it better.
The multivariate data that is the original input for any grand tour visualization is a (finite) set of points in some high-dimensional Euclidean space.
Suppose that for some population of 1000 people, each person is asked to provide their age, height, weight, and number of nose hairs.
A grand tour "method" is an algorithm for assigning a sequence of projections onto (usually) 2-dimensional planes to any given dimension of Euclidean space.