What use is it to know the strength of earth's magnetic field?

Maps of field strength/direction are relevant to things such as satellites and power infrastructure. Some parts of the field are weaker than others (there is a notable weak area over the South Atlantic) which means some areas of the planet are more exposed to solar storms/cosmic radiation than others. Knowing where those weaker areas are allows mitigation of risk to our technology, for example by shutting down sensitive orbiting science experiments whenever they pass over the South Atlantic.

For magnetic compasses to work properly, you also need to map how the field is changing, since the Earth's N-S dipole wanders around to some extent. Compasses also have to balanced for a particular region to take in to account of the vertical component of the field.

By measuring palaeomagnetism in rocks, and comparing the inclination of the remnant magnetism to the inclination of the present field (or at least an idealised version of it), it is possible to estimate the palaeolatitude the rock formed at, which is one of the bases for past continental reconstruction.

Direction is, of course, essential for navigation.

The change in strength illuminates the dynamo in the outer core, and can signal a magnetic reversal.

For example, the magnetic field has weakened some 10% in recent decades and is weakening pretty quickly. This concerns some because it is the magnetic field that protects Earth from the solar wind. If a reversal occurs within the next several centuries, some fear the solar wind will endanger life. I am not so sure a reversal is a big concern, however. There are no extinction events that correlate with reversals, and hominid evolution has occurred through at least several dozen reversals.

Animals use the earth's magnetic field. Man can use it as well.