What is an unambiguous language in the sense of Schützenberger?
Jean Berstel maintains a website with Schützenberger's collected papers. You can access the original paper (in French) here.
A definition of the unambiguous product you are referring to in English is given by Pin in Syntactic Semigroups, p.30:
"The product $L = L_0a_1L_1 \cdots a_nL_n$ is unambiguous if every word $u$ of
$L$ admits a unique factorization of the form $u_0a_1u_1 \cdots a_nu_n$ with $u_0 \in L_0, \cdots, u_n \in L_n$." 
I recommend reading the following survey by Diekert, Gastin and Kufleitner for more background information. They refer to the concept of unambiguous product as "unambiguous monomial".


References:


J.-E. Pin, Syntactic semigroups, Chap. 10 in Handbook of language theory, Vol. I, G. Rozenberg and A. Salomaa (éd.), Springer Verlag, (1997), 679-746.
Volker Diekert, Paul Gastin, and Manfred Kufleitner. A survey on small fragments of first-order logic over finite words. International Journal of Foundations of Computer Science, 19(3):513-548, June 2008. Special issue DLT 2007.