Visual flight rules (VFR) are a set of regulations which allow a pilot to operate an aircraft in weather conditions generally clear enough to allow the pilot to see where the aircraft is going. Specifically, the weather must be better than basic VFR weather minimums, as specified in the rules of the relevant aviation authority. If the weather is worse than VFR minimums, pilots are required to use instrument flight rules.
VFR require a pilot to be able to see outside the cockpit, to control the aircraft's attitude, navigate, and avoid obstacles and other aircraft. 
To avoid collisions, the VFR pilot is expected to "see and avoid" obstacles and other aircraft. Pilots flying under VFR assume responsibility for their separation from all other aircraft and are generally not assigned routes or altitudes by air traffic control. Near busier airports, and while operating within certain types of airspace, VFR aircraft are required to have a transponder to help identify the aircraft on radar. Governing agencies establish specific requirements for VFR flight, including minimum visibility, and distance from clouds, to ensure that aircraft operating under VFR are visible from enough distance to ensure safety.
From a regulatory perspective, airspace is categorized as controlled and uncontrolled. In controlled airspace known as Class B for example (note that Class B does not exist in the UK), Air Traffic Control (ATC) will separate VFR aircraft from all other aircraft. In most other types of controlled airspace, ATC is only required to maintain separation to aircraft operating under instrument flight rules (IFR), but workload permitting will assist all aircraft. In the United States, a pilot operating VFR outside of class B airspace can request "VFR flight following" from ATC. This service is provided by ATC if workload permits it, but is an advisory service only. The responsibility for maintaining separation with other aircraft and proper navigation still remains with the pilot. In the United Kingdom, a pilot can request for "Deconfliction Service", which is similar to flight following.
Meteorological conditions that meet the minimum requirements for VFR flight are termed visual meteorological conditions (VMC). If they are not met, the conditions are considered instrument meteorological conditions(IMC), and a flight may only operate under IFR.
IFR operations have specific training requirements—usually placing a pilot in simulated IMC environment using a view limiting device and recency of experience, equipment, and inspection requirements for both the pilot and aircraft. Additionally, an IFR flight plan must usually be filed in advance. For efficiency of operations, some ATC operations will routinely provide "pop-up" IFR clearances for aircraft operating VFR, but that are arriving at an airport that does not meet VMC requirements. For example, in the United States, at least California's Oakland (KOAK), Monterey (KMRY) and Santa Ana (KSNA) airports do so routinely when a low coastal overcast forces instrument approaches while essentially the entire state of California is basking in sunshine.
Full article ▸