The “height” or “breadth” of a church is a reference in more popular understanding to how elaborate or solemn ritual is. High Church uses chant and incense. Low Church does not. Broad Church may use these in worship on high holy days only.
Differences may obtain in other matters of ritual as well (e.g., what vestments are used), but in theology the “height” of a church is really a reference to how “high” one holds the Church to be in authority. High Church places more emphasis on sacraments than on preaching, for example, but the distinctions are at best very diffuse. Grace is considered to be a “high” parish within the diocese.