Mainly three : they make room for for 'multiplicity, incommensurability, and local consensus'. (Jean-François Lyotard & Niels Brügger, 'What about the Postmodern? The Concept of the Postmodern in the Work of Lyotard', Yale French Studies, No. 99, Jean-Francois Lyotard: Time and Judgment (2001), 84.)
Grand narratives, for reasons with which you will be familiar, are ruled out by Lyotard. But different groups and individuals still have ideas about the subjects that grand narratives were about - justice, religion, democracy, the direction of history and so on. Any idea of constructing a grand narrative that can achieve consensus about such things is a fantasy. Yet 'little narratives' are possible - the different ideas of different groups and individuals which are irreducibly plural or multiple (Judaism, Christianity and Islam will never agree), incommensurable (the God of Islam is not the God of Christianity, and neither is the God of Judaism if we look carefully), and enjoy local consensus (Judaism, Christianity and Islam) bond and join sub-sets of different communities in coherent forms of life. This is how social life is, and 'little narratives' are intrinsic to it. If we consider them clearly, they embody the cultural data of social life after the age of grand narratives. Also, while they do not agree, they are not inherently antagonistic. A culture can accommodate them all.
This is a free reading of Lyotard but I think it conveys what he is getting at with his idea of 'little narratives' and the benefits they carry.