He mentions that Haman wanted to cut us off from being able to access HaShem's infinite Hesed, (loosely translated: Kindness) a light so pure that it cannot be affected, changed, or tainted. It reaches from one end of the world to the other and eradicates all trace of evil. For this reason, for fear of eradication, Haman wanted to separate us from it, HaShem's infinite Hesed.
How did he want to do this in practice? To begin with, how does one connect to HaShem's infinite Hesed? We serve HaShem with excitement and heat. Haman and Amalek, they're power over us is to cool us off, try and bring us back to 'cool' reason, 'cold logic.' To try and ruin the 'heat of the moment.' When we devote ourselves totally and wholly to HaShem with passion and heat, in that place, we can connect to the root of our souls, forever bound up in HaShem's infinite Hesed, from that place all the evil, all the klippot melt away, and Haman is no more.
I think we can see this in practice through Esther HaMalka coming before the king, at great personal risk and for the sake of the nation, from that moment on, we see Haman's actions are no longer his own and a chain of uncontrollable events lead to his almost immediate downfall. The Rebbe went further in explaining the idea, more technical and more detailed, but that's not for me to give over here.
I believe this also explains why it is we are required to get drunk on Purim, to be filled with the heat of love and excitement in performing HaShem's mitzwoth. It's no coincidence that most of the mitzwoth of the day are bound up in Hesed, acts of kindness. The drink takes away the edge of the "cold logic," the cooling effect of Amalek.
One more thing that was never clear to me on Purim was the mitzwah of hearing the megillah, without missing a single word. The rest of the day is about losing da'at, about not being able to maintain an intellectual relationship but rather an emotional, in a way deeper, one. So, it's striking that we are required, on the very same day, to follow, with perfect precision and focus, a text being read aloud. In the context of our tremendous and unfailing love for HaShem this mitzwah can come into focus: When we love someone, we can't take our eyes or ears off them, every word every gesture is not only pleasing, but also vital. If we can connect to the love of HaShem inherent in the day of Purim, then listening to every word of the megillah comes as a freebie, we wouldn't pass up a single word in the story of how He saved us, everything He did for us.