What does each of the Select By Location methods mean?

Answer

Intersect is the most generic operator. As its name implies, it returns any feature that geometrically shares a common part with the source feature(s).

There are a few other operators that are equivalent to intersect for specific uses, for instance:

Are identical to, when comparing point features. 

Are within a distance of, when specifying no buffer or a buffer of 0.

The within a distance operator creates a buffer, or buffers, with a size equal to the distance specified around the source feature, or features, and returns all the features intersecting the buffer, or buffers.

Its typical use would be to retrieve cities within a distance of a river or railroad, shops or business within a distance of a town, and so on.

For a feature to be considered as completely containing another feature, each point in the geometry of the source feature must fall inside the geometry of the target feature, excluding its boundaries. For instance, a polygon representing the United States completely contains the state of Kansas but not Texas, because the southern Texas boundaries overlap the country boundary.

The target feature must be a polygon.

For a feature to be considered as being completely within another feature, each point in the geometry of the target feature must fall within the geometry of the source feature excluding its boundaries. This is the reverse operator from Completely contain. For instance, when using this operator, Wyoming is completely within the United States but Montana is not, as its northern boundaries overlap that of the country.

The source feature must be a polygon or a buffer must be applied around point and line features to use this operator.

A target feature is selected by this operator if the centroid of its geometry falls into the geometry of the source feature or on its boundaries.

With this method, the source and target features are considered as sharing line segments if their geometries have at least two contiguous vertices in common.

The source and target features must be either lines or polygons.

A target feature is returned by this function if its geometry shares line segments, vertices or endpoints with the geometry of the source feature.

The source and target features must be either lines or polygons.

If one of the features is a polygon, an additional requirement is that no part of the geometry of the other feature can be completely within the geometry of the polygon. The geometry of the other feature can only touch the boundaries of the polygon but not the inside.

Two features are considered identical if their geometries are strictly equal. The feature types must be the same. For instance, this operator can be used to compare two polygon layers, but comparing a point layer and a polygon layer for identity always returns an empty selection.

For this operator, the boundaries of the source and target feature must have at least one edge, vertex or endpoint in common but must not share a line segment.

The source and target features must be either lines or polygons.

This method differs from the 'Completely contain' method in that the geometry of the source feature must fall inside the geometry of the target feature including its boundaries.

A polygon representing the United States contains the state of Texas even though their boundaries overlap along the southern border of the country.

The target feature must be a polygon.

This method differs from the 'Are completely within' method in that the geometry of the target feature must fall inside the geometry of the source feature including its boundaries.

For example, using this operator, Montana is selected even if its boundaries partly overlap that of the country.