Assimilation is a process involving two words when spoken in sequence. We are modifying the sounds between the first and second words so they combine (assimilate) to make another sound. The joining of the two words is a type of connected speech. We could say it makes the words sound more similar and so more fluid in speech.  The best way to understand it is by listening to examples and using the phonetic table. It is a natural understanding that comes with increased fluency. Two phonemes come together and form one phoneme. That is a new sound.