Simply stated, seismic inversion is the process of determining what physical characteristics of rocks and fluids could have produced the seismic record you are viewing. Another way to look at it: we are trying to determine the input by looking at the output. Transforming a noisy, processed seismic trace into a density log or a sonic log is the inverse of transforming these two logs into a synthetic seismogram, hence the name inversion. Inversion is the “flip side” of forward modeling.
In many cases the physical parameters of interest are impedance, velocity and density although people have been know to invert for more exotic parameters like Poisson’s ratio, incompressibility (Lambda), shear modulus or rigidity ( Mu ), etc. It is also possible to move on to an estimation of properties that are more familiar like porosity or even sand/shale ratios or gas saturation.
In practice, the common methods of performing seismic inversion attempt to remove the effects of the wavelet. This leads to a higher resolution display and in this sense acoustic impedance inversion can be thought of as a form of deconvolution.
Another way to approach the inversion concept is to realize that standard acoustic impedance inversion requires model building that usually incorporates well log data from all the nearby wells. The forward model is created by carefully calibrating the seismic data with log-based synthetic seismograms. Therefore the final inversion result is a data set that ties all the wells and also honors all the seismic data. In this sense, inversion can also be considered a sophisticated method of integrating well logs and seismic data.