Here is what the UK instructions to controllers says:
1 Introduction
1.1 It is recognised that a need exists to warn pilots of the presence of water on a runway. The Aerodrome Authority is responsible for assessing runway surface conditions.
1.2 When the presence of water on a runway is brought to the attention of the controller, the information shall be passed to aircraft.
2 Reporting Wet Runways
2.1 The presence or otherwise of surface water on a runway is to be reported on the RTF and ATIS, in plain language, using the following descriptions:
Reporting Term Surface conditions
DRY The surface is not affected by water, slush, snow, or ice.
NOTE: Reports that the runway is dry are not normally to be passed to pilots. If no runway surface report is passed, pilots will assume the surface to be dry.
DAMP The surface shows a change of colour due to moisture.
NOTE: If there is sufficient moisture to produce a surface film or the surface appears reflective, the runway will be reported as WET.
WET The surface is soaked but no significant patches of standing water
are visible.
NOTE: Standing water is considered to exist when water on the runway surface is deeper than 3mm. Patches of standing water covering more than 25% of the assessed area will be reported as WATER PATCHES.
WATER PATCHES Significant patches of standing water are visible.
NOTE: Water patches will be reported when more than 25% of the assessed area is covered by water more than 3mm deep.
FLOODED Extensive patches of standing water are visible.
NOTE: Flooded will be reported when more than 50% of the assessed area is covered by water more than 3mm deep.
2.2 When reported, the presence or otherwise of surface water on a runway will be assessed over the most significant portion of the runway, i.e. the area most likely to be used by aircraft taking-off and landing. This area may differ slightly from one runway to another but will approximate to the central two-thirds of the width of the runway extending longitudinally from a point 100 m before the aiming point to 100 m beyond the aiming point for the reciprocal runway. The assessed area may be different on runways with a displaced threshold or other unusual configuration, e.g. starter extension. The Aerodrome Authority is responsible for determining the exact dimensions and location of the area that is assessed.
2.3 Reports of the runway to be used include, sequentially, the conditions in each third of the assessed area. For example, “Runway surface is wet, water patches, wet” or “Runway surface is wet, wet, wet”.
2.4 A brief description of any water patches greater than 9mm in depth, which may affect engine performance, will be appended to a runway surface condition report. In such conditions, further information on the location, extent and depth of the water patches will be available from the Aerodrome Authority.
2.5 A brief description of any notable quantity of water outside the assessed area, e.g. water collected at the runway edge, will be appended to a runway surface condition report.
I though the same information was in the AIP but I couldn't find it when I had a quick look just now.
I think these rules came in when JAR-OPS was introduced and pilots started asking whether the runway was contaminated or not. This caused some confusion - from what I recall, JAR-OPS considered a runway contaminated (and thus needed the use of particular sets of performance data) when it was wet or worse whereas airports and ATC generally thought of contaminated as covered in de-icer or similar.
From where I sat in the day job at the time it looked like JAA had developed a fine set of rules for aircraft operation for assessing runway state.......but didn't look at what ICAO said would actually be reported by airports and ATC!