The explanation I’ve always had- I think this was from some official source but I could have just made it up.
Starfleet ships use EPS (Electro-Plasma System) to route power around the ship in the form of electro-plasma (a highly energized form of plasma). The warp core generates a lot of this plasma, which is piped through conduits to various devices around the ship. The EPS system and its related systems generate a lot of treknobabble about ‘scrubbing plasma conduits’ (apparently done from the outside using a field generator tool, but still boring), ‘replacing plasma relays’ (the valves that route plasma around, apparently they go bad frequently); problems like ruptured plasma conduits are dangerous and require immediate repair, etc.
Because this all works in a grid system, whenever the ship takes damage (especially energetic damage like weapons fire) the EPS conduits can carry energy spikes all over the ship. That’s why as the ship takes damage you see random small explosions and sparks all over the place- something hits or spikes the EPS grid and the shockwave ends up, well, wherever in the grid it ends up.
Of course many EPS conduits go to bridge terminals, especially as those terminals may have direct connections to the ship systems in question.
Of course in reality this would be seen as a horrible safety risk, and a bridge terminal that could probably run on a car battery shouldn’t have explosive plasma running through it especially when it can explode and harm the operator. In fact one could argue a safe starship should keep all EPS stuff as far away from any essential human-inhabited areas of the ship as possible (especially the bridge).
One counter to that might be that perhaps the consoles actually play some role in EPS switching, but that seems a bad tradeoff to me.