a bridging oxygen
A bridging oxygen is an oxygen atom that acts as a hinge between two network polyhedra, bonded to a network cation on each side. In a silica glass it is the O in an Si-O-Si linkage: one oxygen tying two silicon tetrahedra together at a shared corner. Think of it as the peg that joins two Lego bricks. Every bridging oxygen is a rung in the ladder of connectivity, and it is the sum of all these bridges that makes the glass a single, continuous, load-bearing network rather than a pile of loose pieces.
In pure fused silica, every oxygen is a bridging oxygen. Each silicon owns four oxygens, and each of those oxygens is shared with a neighbouring silicon, so on average there are two silicons per oxygen and the network is fully polymerized, connected in all directions with no loose ends. This total bridging is exactly why pure silica is so stiff, so high-melting, and so resistant to chemical attack: to move or dissolve anything you must break a strong Si-O bridge, and there are no weak points to start from.
The count of bridging oxygens is the single best measure of how connected, and therefore how viscous and durable, a glass is. Every network-modifier you add replaces bridging oxygens with non-bridging ones, lowering the bridge count and loosening the web. Glass scientists track this with the ratio of non-bridging oxygens per network former: a fully bridged silica has none, while a heavily fluxed soda-lime glass has many. So bridging versus non-bridging oxygen is the accounting that connects composition to every practical property of a glass.
Count the bridges to predict the viscosity. Fused silica is all bridging oxygen, so its working temperature is punishingly high, near 2000 degrees C. Start adding soda and each unit swaps two bridges for dead-ends; by the time you reach ordinary window glass the bridge count has dropped enough that the working temperature has fallen to a manageable 1000 degrees C. Same network, just fewer intact rungs.
More bridging oxygens means a more connected, stiffer, more durable glass; modifiers cut bridges and soften the glass.
Bridging oxygen is a connectivity idea, not a special kind of atom. The very same oxygen becomes non-bridging the instant a modifier breaks one of its two bonds; nothing about the oxygen itself changes but its number of network neighbours.