Before us is the second Mishnah in the second chapter of Maseches Pesachim, which deals with the law of chametz that was owned by a Jew over Pesach.
"Chametz shel nochri she'avar alav haPesach - mutar b'hana'ah, v'shel Yisrael - asur b'hana'ah, shene'emar: 'V'lo yera'eh lecha se'or'"
"Chametz shel nochri she'avar alav haPesach - mutar b'hana'ah":
Chametz that belonged to a non-Jew during the days of Pesach may be used by a Jew for benefit after Pesach, since there is no prohibition at all upon a non-Jew keeping chametz in his possession.
"V'shel Yisrael - asur b'hana'ah":
Chametz that belonged to a Jew during the days of Pesach may not be used for benefit in any manner whatsoever after Pesach. This is what is called 'chametz she'avar alav haPesach'.
"Shene'emar: 'V'lo yera'eh lecha se'or'" - what is the Mishnah teaching us by bringing this verse?
Identifying the transgression: The verse teaches that the Jew who kept chametz in his possession violated the prohibition of "V'lo yera'eh lecha se'or", and on account of that transgression the Sages decreed a rabbinic prohibition against deriving benefit from chametz that he owned over Pesach.
A source for a precise reading: The verse is not coming to identify the transgression, but rather to teach us a precise reading of its wording: "V'lo yera'eh lecha se'or" - it is specifically the Jew who is forbidden to keep chametz, whereas the non-Jew is permitted to do so. For this reason, chametz that belonged to a non-Jew is not problematic at all, and it may be used after Pesach.
In summary: In this Mishnah we learned the distinction between the chametz of a non-Jew and the chametz of a Jew that remained in their possession over Pesach: the chametz of the non-Jew is permitted for benefit, since a non-Jew is not commanded regarding the keeping of chametz, whereas the chametz of the Jew is forbidden for benefit. Regarding the citation of the verse "V'lo yera'eh lecha se'or", we saw two explanations: it identifies the prohibition that the Jew violated, on account of which the Sages penalized him and forbade the chametz for benefit, or it is a precise reading of the word "lecha" - that only a Jew is forbidden to keep chametz.