What is the official definition of a feature in signal classification? Nowadays read any paper or reference on signal classification scheme you would invariably come across the term "feature". What does feature mean exactly? What is considered a time domain feature, what is considered a frequency domain feature and what is considered a phase domain feature?

I would be glad if someone can clarify this concept for me once and for all.
Features are properties of the signal used to describe it in some way. Sometimes the term "descriptors" is used, for example MPEG-7 audio-visual description standard: 



Time domain features are computed from the audio waveform, while frequency-domain or spectral features are derived after performing an FFT. 

You should look through a feature-extraction software package like Yaafe, to get some practical intuition. There are also many tutorials and papers online for further learning.