Being and non-being.
The abyss is common in mystical and spiritual experiences. Churchill is here obviously being intentionally irreverent for humorous effect.
In essence, the abyss is the terrifying lack of ground and security, the void, the emptiness or lack of being which confronts consciousness when it is in the process of radical change. That is, non-being in the form we engage directly, rather than as a concept.
The byss is a word presumably meaning the opposite of abyss, the positive side of what abyss negates. That is, the content of everyday consciousness, the solid, comforting world of objects and entities we rely on as the commonplace being.
All these things are held at arms length by philosophy, but the real passage through them is the driving force behind such explorations. Only by actual experience do they become alive and active.
What we take for granted as having real being, here we're calling it the byss, alternates and interpenetrates beyond our normal capacity to comprehend or control with the abyss.
Everything is two-sided in reality, a truth that cuts across all traditions. The known and unknown, dependent and spontaneous arising, being and non-being, relative and absolute, byss and abyss.
This phrase also appears in William James's masterpiece The Variety of Religious Experience where Jacob Boehme is quoted as saying:
In one quarter of an hour I saw and knew more than if I had been many
years together at an university. For I saw and knew the being of all
things, the Byss and the Abyss, and the eternal generation of the holy
Trinity, the descent and original of the world and of all creatures
through the divine wisdom.