An intermediate conclusion is something in an argument that functions both as a reason and as a conclusion.

To function as a reason, it must offer support to the main conclusion of the argument (or to another intermediate conclusion).

To function as a conclusion, there must be something else in the argument that lends it support.

Take, for example, the following argument: “Your face is covered in chocolate, so it must have been you that ate my cake, so you owe me a cake.” The main conclusion of this argument is the final clause: “You owe me a cake.” This is supported by the previous clause, which is therefore functioning as a reason, “it must have been you that ate my cake.” This clause, though, is also supported by the previous clause, “Your face is covered in chocolate”, so it is both a conclusion and a reason; it is an intermediate conclusion.