A medium for thinking is a mode of expression. It's a format, a specific structure to the information, that allows us to re-present our thinking in that medium.
What is a Medium?
Ted Nelson's definition of a medium
"A medium is a set of presentation elements, and relations among them, that may be used by a person to create an object, environment or experience for someone else." Ted Nelson in The Crafting of Media
"presentation" - mediums for thinking are specifically for re-presenting our thoughts (are thoughts abstractions or are they always embodied in a specific form?)
"relations among the elements" - the inter-relationships of the symbols in the medium is pretty much the hard part about crafting the medium
"used to create" - a medium is a generative thing. What is created by a medium is not the medium itself, but an instance of it.
"an object, an environment, an experience" - Mediums may be experiential, they may create a "surround sound"-like environment, or they may be a specific concrete object.
"for someone else" - may include the same person at a later time
Marshall McLuhan's Definition
Marshall McLuhan
Media is seen as an extension of our senses, and our very selves. Or, really, any new technology.
"All technologies mediate our communication; their forms or structures affect how we perceive and understand the world around us."
from the wikipedia article
"how we perceive and understand the world" - again, a medium is a way that we present our thoughts.