Multilevel models (also known as hierarchical linear models, nested data models, mixed models, random coefficient, random-effects models, random parameter models, or split-plot designs) are statistical models of parameters that vary at more than one level (Wikipedia). They are very useful in Social Sciences, where we are often interested in individuals that reside in nations, organizations, teams, or other higher-level units. Next to their individuals characteristics, the characteristics of these units they belong to may also have effects. To take into account effects from variables residing at multiple levels, we can use multilevel or hierarchical models.
Michael Freeman, a faculty member at the University of Washington Information School. made this amazing visual introduction to hierarchical modeling:
If you want to practice hierarchical modeling in R, I recommend the lesson by Page Paccini (first video) or the more elaborate video series by Statistics of DOOM (second):