We begin chapter 5 of Maseches Nazir. Mishnah 1 deals with the question of hekdesh made in error: a person who consecrated something based on a mistaken understanding, and the reality turned out to be different from what he assumed when he made his declaration - does the consecration take effect? On this question Beis Shammai and Beis Hillel disagree.
The dispute between Beis Shammai and Beis Hillel:
"Hekdesh ta'us" - Beis Shammai say that the consecration takes effect, even though the person was mistaken and things are not as he thought they were when he declared that the item should be consecrated. Despite the error, the item is holy.
"Eino hekdesh" - Beis Hillel disagree and say: if the consecration was made out of a mistake and a mistaken understanding, the consecration does not take effect.
The example in the Mishnah:
The Mishnah explains the dispute through a practical case: a person says "Shor shachor sheyeitzei mibeisi rishon harei hu hekdesh" - the black ox that leaves my house first is hereby consecrated - and a white ox came out. Beis Shammai say it is hekdesh: the consecration takes effect, even though it was not the black ox that came out but the white one. Beis Hillel say it is not hekdesh, since the entire consecration rested on a mistake.
The Gemara's explanation of the case:
The Gemara clarifies that the case is speaking about a person who owned only one black ox. Therefore, when he said "the black ox that leaves my house first," he did not mean the first among several black oxen; he assumed that his black ox would be the one to leave the house first. The mistake, then, was in his assumption - he thought the black ox would come out first, and in fact the white ox came out.
Therefore: even though the white ox came out, contrary to what he assumed would happen, according to Beis Shammai it is considered hekdesh; and according to Beis Hillel it is not hekdesh, since what he thought would happen did not actually occur.
In summary: in this Mishnah we learned the dispute between Beis Shammai and Beis Hillel regarding hekdesh made in error - Beis Shammai uphold the consecration even though it was made mistakenly, while Beis Hillel nullify it. The example is a person who consecrated the black ox that would leave his house first, and the white one came out; and according to the Gemara's explanation, he had only a single black ox, and his mistake was in assuming that it specifically would come out first.