What geographical area does a METAR cover? According to the FAA's AC 00-45G section 3.1, a METAR is defined:


  Aviation Routine Weather Report (METAR) is the primary observation code used in the U. S. to
  satisfy World Meteorological Organization (WMO) and International Civil Aviation Organization
  (ICAO) requirements for reporting surface meteorological data. A METAR report includes the
  airport identifier, time of observation, wind, visibility, runway visual range, present weather
  phenomena, sky conditions, temperature, dew point, and altimeter setting. Excluding the airport
  identifier and the time of observation, this information is collectively referred to as “the body of the
  report.” As an addition, coded and/or plain language information elaborating on data in “the body
  of the report” may be appended to the end of the METAR in a section coded as
  
  “Remarks.” The contents of the “Remarks” section vary with the type of reporting station. The
  METAR may be abridged at some designated stations only including a few of the mentioned
  elements.


What doesn't appear to be defined is exactly what area the METAR covers. It's understood that a METAR is a reporting for a particular station's current conditions at a particular time, but is there a more discrete definition for where the METAR's conditions can be expected?

The definition of a TAF specifically states that the forecast conditions are expected in an area around the reporting station with a radius of 5 statute miles. The METAR has no such specification that I can find.
Geographically METARS are for a single specific location (the station identified in the report).

An automated METAR with no human supervision covers the conditions within approximately 6 inches of the weather station reporting it (for example, a badly positioned AWOS/ASOS station may be shielded from wind in some directions which affects what it reports).

A manual (or manually augmented) METAR covers the conditions the weather observer can physically see (clouds, precipitation, visibility, etc.) in addition to the ones they can measure (temperature, dew point, barometric pressure), which are valid for the point of measurement. 



Practically speaking if the weather station is positioned well a METAR (like a TAF) is probably fairly representative of conditions within 5 miles, assuming there are no geographic features such as mountains which may mess with the weather. The data is still still "useful" within about 20 miles (e.g. KMTP uses the weather reported by KHTO, about 17 miles away), though you should obviously cross-check it - in that example the winds at Montauk (right on the water) can be noticeably different from the winds at East Hampton (further inland).

Some information is broadly useful over a wider area. FAR 91.121 requires you to set your altimeter to the value reported by a station "within 100 nautical miles" of your position when you're operating below 18,000 feet because things like barometric pressure tend to affect relatively large areas.