We are in chapter 4 of Maseches Challah. This mishnah follows directly from the previous one. In the second half of that mishnah we learned of the dispute between Rabbi Akiva and the Chachamim as to whether separating challah from a dough containing only one kav, which is less than the amount that obligates in challah, is effective. Rabbi Akiva holds that the separation is effective, provided that afterward the dough is enlarged to the measure that requires challah, and then, retroactively, the separation counts as challah; the Chachamim say that the separation is not effective retroactively.
The case in our mishnah:
"Shnei kabin shenitlah challaso shel zeh bifnei atzmo v'shel zeh bifnei atzmo, v'chazar va'asa'an isah achas" - the case is of two kavin, from each of which challah was separated on its own. Neither kav by itself was obligated in challah, since it does not contain the required measure, and nevertheless challah was separated from it. Afterward the two kavin were joined and became a single dough, and now the dough does contain the measure that obligates in challah.
In practice this is the very case discussed in the previous mishnah, except that here it has already been carried out: the two kavin have already been joined into one dough, and challah has already been separated from each of them.
"Rabbi Akiva poter" - the newly combined dough is exempt from separating challah, because the challah that was separated earlier from each of the doughs counts retroactively as challah, and it now takes effect on the combined dough. This follows his position that separating challah from less than the required measure is effective, at least retroactively.
"V'chachamim mechayvin" - the challah separated earlier accomplished nothing at all. Once the two kavin were joined and the measure for challah was created, a new obligation to separate came into being that did not exist before, and therefore challah must be separated from the new dough.
The result: Rabbi Akiva's stringency in the previous mishnah, that separating challah from a single kav is considered effective and takes effect retroactively, is itself the basis for his leniency here. Because of that very stringency he rules leniently that the new dough, the two kavin that were united, is not obligated in challah, since the challah separated earlier has already taken effect upon it, and there is no need to separate challah from it after it was joined together.