What is defined as "day VFR" under EASA rules?
It's by opposition to Night VFR (NVFR) which allows to fly by night in visual meteorological conditions. So the answer will focus on NVFR, rather than on day VFR.

EASA harmonization over EU countries is done by enforcing Standardised European Rules of the Air (SERA). SERA states that a night flight must be conducted in IFR, and therefore the crew must hold an Instrument Rating.

Prior to SERA, some countries did not allow VFR at night for security reasons (aircraft not visually identifiable, and no transponder), but other did, that's the case for the UK that I'll use as an example here.

When implementing SERA, EU countries can use acceptable means of compliance, as described in ED Decision 2013/013/R and its annex.


NVFR is implemented (or denied) in EU country by country. So rules may differ between countries. UK example:


UK license can be extended for NVFR.
More for UK NVFR: Safety Notice: SN-2012/007.
In practice, VFR at night is permitted in accordance with SERA requirements. Aircraft leaving the vicinity of an aerodrome must maintain 2-way communication with ATC and file a flight plan. The process of 'booking out' is still accepted as an alternative method to filing a formal paper or electronic flight plan in certain circumstances. Similarly, abbreviated flight plans filed in flight are still permitted. There are also more restricting weather minima:


Minimum cloud ceiling of 1500 ft AMSL
Flight visibility of 5 km, or 3 km in the case of a helicopter flying outside controlled airspace
Maintain sight of the surface when flying at 3,000 ft AMSL or below
Minimum height of 1000 ft (or 2000 ft if over high terrain) above the highest fixed obstacle within 8 km of the aircraft except when taking off or landing 



Night is defined for  this purpose:


e.g. for UK in Air Navigation Order 2009 Art. 255:


  'Night' means the time from half an hour after sunset until half an
  hour before sunrise [...] at surface level.


Aircraft must be compliant for NVFR, e.g. this equipment is required:


artificial horizon
Instrument Lighting
Landing Light
Position and Anti Collision Lights





In countries where NVFR is not allowed, IFR applies at night.