Basically, the idea is that we tend to build mainly single-family homes on large lots (suburban model) or medium to large apartment buildings (urban model) in the United States. Just like large-scale suburbia in the U.S. emerged as an attempt to hybridize the urban and the rural in the wake of the Industrial Revolution of the 19th Century, what if we could hybridize the suburban and the the urban to create an environment that is denser and has more transportation and housing options than suburbia, but still aesthetically resembles suburbia, and doesn't freak out the average American?
The Missing Middle philosophy attempts to do this by emphasizing housing types that we often overlook: small-lot detached houses, duplexes, triplexes, fourplexes, bungalow courts (i.e. clusters of small single-story detached cottages on a single lot), townhomes (i.e. homes of two to three stories with at least one side wall shared with an adjacent unit), live-work units (e.g. a building with a residential floor over a retail floor) and courtyard apartments. In designing these buildings, one is supposed to match the appearance of a neighborhood of detached houses by not exceeding three stories in height, matching setbacks, and considering how architectural design can make multi-unit buildings appear as a single housing unit (e.g. by making a fourplex that looks like a large mansion). Key to making this all work is local governments being willing to back off of suburban-style parking requirements. High parking requirements can make these housing types either too hard to build, too expensive to build, or aesthetically unappealing (since sites get dominated by pavement or structured parking). Parolek recommends providing no more than one off-street parking space per unit.
The Missing Middle is important because it makes the point that not everybody who is seeking a more walkable environment is comfortable with a full-blown urban lifestyle. However, there may be many people who are willing to try living in a place that has a suburban feel, but a bit of urban functionality. Baby steps can be a good thing :)