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The moment any celestial body crosses over your longitude line (your meridian), bearing precisely due north or south. A body approaching your meridian from the east will have a large LHA (local hour angle) that reaches 360° and starts over at 0° just as it crosses the meridian at its peak height in the sky.
Meridian passage of the sun is called local apparent noon (LAN).
Meridian passage of other bodies do not have a special name, although looking north, meridian passage of circumpolar stars crossing your meridian over the top Polaris headed west are described as upper transit (at their peak height in the sky), while those crossing the meridian below Polaris headed east (at their lowest point in the sky) are described as crossing your meridian at lower transit.
Once you have found your latitude this way (from any body, though sun is by far most common) it is plotted on the chart as a line of position and used with other sights to find a fix.
See: Local Apparent Noon.