The first Mishnah on the page concludes with a ruling that if a ka-zayit – an olive size piece of the sacrifice – is brought outside the Temple, that would be sufficient to be considered a sacrifice that took place outside, with all of the associated repercussions.
In the second Mishnah on the page we learn that other types of Temple services also cannot be performed outside of the Beit ha-Mikdash. Therefore, if a ka-zayit from one of the various types of meal-offerings were sacrificed outside of the Temple, the individual who performed the service would be held liable. In this case, however Rabbi Eliezer rules that a ka-zayit would not be enough, and only if the entire meal offering were brought outside would the service be considered to be significant.
Rashi explains that Rabbi Eliezer does not disagree with the first Mishnah, and accepts that even a ka-zayit would be sufficient in the case of an animal sacrifice for the person to be held liable if it is done outside the Temple. The distinction between the cases is that in a typical animal sacrifice, even if some of the meat is missing and is not sacrificed, nevertheless the korban is valid. Therefore, if such an offering is performed outside of the Temple, it is forbidden. Meal-offerings, on the other hand, are not valid unless they are brought in their entirety, so bringing a partial meal-offering outside of the Temple is not a significant act. He agrees, however, that if the meal-offering were brought in the Temple, and a ka-zayit of the offering was left over and brought outside of the Temple, then the person doing so would be held liable, since in that case the meal-offering was completed outside of the Temple in a forbidden manner.