What is life-continuum?
life-continuum is Bhavanga-citta. It's the filler thought moment/moments between every 2 thoughts/experiences. It keeps you from dying when the senses cannot provide an object to the mind. When you are in dreamless sleep, your mind mostly has Bhavanga-cittas. 

It's the first thought moment in your life and the last thought moment of the previous life. It is a resultant thought moment, thus Karmicly neutral. For humans and above, it's always a result of good Karma. For hell-beings, it's a result of bad Karma.