The result from 1 RET 0 / will be the formula 1 / 0. The "function" `/' cannot be evaluated when its second argument is zero, so it is left in symbolic form. When you now type 0 *, the result will be zero because Calc uses the general rule that "zero times anything is zero."
The m i command enables an infinite mode in which 1 / 0 results in a special symbol that represents "infinity." If you multiply infinity by zero, Calc uses another special new symbol to show that the answer is "indeterminate." See section Infinities, for further discussion of infinite and indeterminate values.