The Edict of Milan--along with Constantine's other measures (such as the church-building campaign you mention)--brought stability to Christianity and paved the way for the later institutionalization of Christianity in the Roman Empire. Prior to Constantine, Christians had endured sporadic persecution (most notably from Nero, Diocletian, and Galerius). While Christianity grew even during periods of persecution, the Edict of Milan gave Christianity equal status to other Roman religions, which allowed Christians to "put down roots" without fear of imperial persecution.
Moreover, the Edict of Milan paved the way for Christianity's later institutionalization in the Roman Empire. Strictly speaking, the Edict only gave Christians religious freedom. However, Constantine took an active role in the Christian Church, even convening Church councils. This alignment of church and state continued after Constantine's reign, and Emperor Theodosius I's passage of the Edict of Thessolonica made Christianity the official religion of the Roman Empire in 380.