For reconstructing the phylogenetic tree, we will need to make some assumptions on how DNA or protein sequences change over time. Mathematically, we would expect the 4 nucleotides or the 20 amino acids have equal chances of changing over a fixed course of time (substitution), biologically this is not the case. Many processes prevents this from happening. As a result there are many substitution models that have been developed, called evolutionary models, that make assumptions on how DNA/protein sequences change over time.
Evolutionary models try to explain the complex biological phenomenon as a simple mathematically explainable formula. Although phylogentic tree building programs can estimate all the different parameters of the substitution matrix, it is advantageous to provide a simple, relatively good fitting model for the data in hand to begin with. This ensures characterization of the evolutionary process accurate.
Process of selecting the model: we test our data for fit with a battery of models, perform likelihood ratio tests (LRT), and select the best fitting model by doing statistical tests. It is only appropriate to do this LRT testing when the 2 models compared differs by one or couple of parameters. The process is as follows (source: Posada, D. (2003). Selecting models of evolution. The phylogenetic handbook: a practical approach to DNA and protein phylogeny, 256-282.)