This article is from the Aviation FAQ, by Geoffrey G. Peck email@example.com with numerous contributions by others.
ATP Airline Transport Pilot (the "highest" grade of pilot certificate)
AME Aviation Medical Examiner (U.S.)
FAR Federal Aviation Regulations (U.S.)
CFI Certificated Flight Instructor (see suffixes, below)
COM Commercial (pilot certificate) (see suffixes, below)
IFR Instrument Flight Rules (see below)
PP Private Pilot
PVT Private (pilot certificate) (see suffixes, below)
VFR Visual Flight Rules (see below)
Pilot and instructor certificates may be suffixed with certain
combinations of the following:
A Airplane ME Multi-Engine L Land I Instrument
G Glider SE Single-Engine S Sea
For example, the typical private pilot is "PP-ASEL" or "PVT-ASEL".
Ratings are more complex than this limited explanation -- for
example, Rotorcraft come in two flavors, Helicopter and Gyroplane;
Lighter-than-Air aircraft come in two flavors, Free Balloon and
Airship; and there are specific type ratings for aircraft over 12,500
pounds. One can spend several lifetimes accumulating ratings.
A pilot who does not hold an instrument rating must fly under VFR,
which specify minimum cloud clearance and visibility requirements.
In some countries other than the U.S., VFR flight at night is not
permitted. Pilots who fly under VFR do so by looking out the
window. Flight through clouds is permitted only under IFR, which
requires an instrument rating and an appropriately-equipped
aircraft. Instrument-rated pilots may control the aircraft solely by
reference to instruments, but if they are flying in VMC, they are
expected to look out the window to avoid other aircraft.