What is the official definition of a feature in signal classification?
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.