Geodesy is the science of measuring the size and shape of the earth and its gravitational field.
Some would also include the study of the Earth's magnetic field.
Wolfgang Torge quotes in his 2001 textbook Geodesy (3rd edition) Friedrich Robert Helmert as defining geodesy as "the science of the measurement and mapping of the earth's surface."
As Torge also remarks, the shape of the earth is to a large extent shaped by its gravity field. This applies to the solid surface (orogeny; few mountains are higher than 10 km, few deep sea trenches deeper than that) as it does to the liquid surface (dynamic sea surface topography) and the earth's atmosphere. For this reason, the study of the Earth's gravity field is seen as a part of geodesy, called physical geodesy.