Tinok shenishbah means a small child who was kidnapped by non-Jews. It is an important concept in discussions of the responsibility of non-observant Jews for their lack of observance.
One of the classic sources is in Talmud Shabbat 67b-68a. The Mishnah there speaks about a case in which someone "forgets the fundamental principle of Shabbat", meaning, at first glance that there is such a thing as Shabbat at all.
How on earth could anyone forget that? the Talmud wonders. Two sages answer, that the case is one of a child kidnapped by non-Jews, who therefore grew up without knowing the rudiments of Judaism.
In the Middle Ages, the concept was applied to Karaites, who did not transmit the Oral Torah to their children. In the post-emancipation period it has been applied to secular Jews. This conceptual move was made by religious communities out of an impulse towards love and acceptance; if non-observant Jews simply didn't know any better, then their responsibility was diminished and they were not to be regarded as flagrant, deliberate transgressors.