MFCC is a feature used in Automatic Speech Recognition.To understand the liftering concept , first you need to understand the concept of Cepstral Analysis.

Speech is a mixture of vocal tract and input exitation.Liftering is a method used to separate the vocal tract and the excitation sequence in the frequency domain.You can say that Liftering is somewhat similar to filtering in frequency domain. In filtering , normally we multiply the whole spectrum with a desired rectangular window. Simialrly in liftering also

But your question is far too wide to answer exactly. Refer to the links below.Hope they might be helpful for you to understand.

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