A topographic profile is a cross sectional

Cross section (geometry)

In geometry, a cross-section is the intersection of a figure in 2-dimensional space with a line, or of a body in 3-dimensional space with a plane, etc...

 view along a line drawn through a portion of a topographic map

Topographic map

A topographic map is a type of map characterized by large-scale detail and quantitative representation of relief, usually using contour lines in modern mapping, but historically using a variety of methods. Traditional definitions require a topographic map to show both natural and man-made features...

. In other words, if you could slice through a portion of the earth, pull away one half, and look at it from the side, the surface would be a topographic profile.

Not only does constructing a topographic profile aid in understanding topographic maps, it is very useful for geologists

Geology

Geology is the science comprising the study of solid Earth, the rocks of which it is composed, and the processes by which it evolves. Geology gives insight into the history of the Earth, as it provides the primary evidence for plate tectonics, the evolutionary history of life, and past climates...

when analyzing numerous problems.