When lightning strikes, huge amounts of current flow for a small fraction of a second. The current can reach into the millions of Amperes range. This large current flowing induces voltage into any electrical conductor, such as rail or signal wiring, that happens to be nearby. This induced voltage causes a relay to trip that normally detects a train on the tracks.

My understanding is that induced voltage from lightning near misses causes more damage to devices connected to the power grid than do actual lightning strikes to power lines. Measurements in Florida have found 6,000 Volt spikes on nominal 110 Volt circuits.