Despite decades of studies, the nature of the glass transition remains elusive. In particular, the sharpness of the dynamical arrest of a melt at the glass transition is captured by its fragility. Here, we reveal that fragility is governed by the medium-range order structure. Based on neutron-diffraction data for a series of aluminosilicate glasses, we propose a measurable structural parameter that features a strong inverse correlation with fragility, namely, the average medium-range distance (MRD). We use in-situ high-temperature neutron-scattering data to discuss the physical origin of this correlation. We argue that glasses exhibiting low MRD values present an excess of small network rings. Such rings are unstable and deform more readily with changes in temperature, which tends to increase fragility. These results reveal that the sharpness of the dynamical arrest experienced by a silicate glass at the glass transition is surprisingly encoded into the stability of rings in its network.