The Rambam's sefer halacha which is entitled Mishna Torah is usually referred to by its nickname, the Yad Hachazaka. The letters of the work Yad add up to fourteen in gematria , and there are fourteen different volumes in the Mishna Torah. One of those volumes, the Sefer Hafla'ah, deals with all of the halachos that take effect by a person making a declaration: neder, shavuah, nezirus, etc. Regarding all other matters of hafloah, speaking is required. This is established based on the possuk in Parshas Vayikra that speaks about a person accepting a shavuah "l'vateh b'sfosayim - to pronounce with one's lips." Even if one made up his mind to accept a neder or a shavuah, it is not binding until he pronounces it with his lips.
In Parshas Korach, the Torah records that hafroshas teruma is an exception to this rule. Commenting on the possuk, "v'nechshav lochem terumaschem" the Gemara teaches us that in addition to the correct simple reading of the possuk, the Torah sheb'al peh adds an additional level of interpretation, i.e. that terumah can take effect by the owner of the produce just thinking. There was a common practice in Europe that when the women would bake bread, cake, or cookies and would be mafrish challah, they would recite the beracha over the performance of the mitzvah but would not declare that the little bit of dough that they separated should become challah. Since we assume that challah has the exact same dinim as terumah, the kedushas challah takes effect even though the women never declared it as such, since they clearly had in mind that the little dough that they separated should become challah. Rabbi Akiva Eiger in his commentary on Yoreh Deah quotes from the She'iltos, who lived in Bavel and thus was only mafrish challas chutz la'aretz, that this is not the proper practice, and it would be more correct if after reciting the beracha over the mitzvah of hafrashas challah, women would state that this little bit of dough should become challah.
The Netziv, in his commentary on the She'iltos, develops a fascinating idea to defend the practice of women to bedafka not declare the piece of dough to be challah. The Gemara tells us that just as a nazir is not permitted to come in contact with a meis, so too a person who happens to be located in a cemetery should not accept upon himself a neder nezirus. Why does the Gemara say "just as...so too"? Why are these two things the same? Obviously the Gemara understood that the nature of the prohibition of the nazir coming in contact with the meis is that one is not permitted to bring about a situation where you will have a nazir tamei. Therefore, one who is in the cemetery and accepts upon himself a neder nezirus has brought into existence a situation of a nazir tamei. The Netziv suggests that maybe the same applies to teruma temei'ah. The Gemara understands from the possuk, "Mishmeres terumosai" that one must be careful not to cause teruma to become tamei. Similarly, we ought to say that one who has dough which is tamei is not allowed to be mafrish challah from it because he is bringing into existence teruma temei'ah. Today everyone is tamei and since flour is mixed with water to make dough, it was already huchshar l'kabeil tuma, so the dough will become tamei. This should lead us to say that we are not allowed to be mafrish challah, but that is not possible! Dough or bread that is tamei may not be eaten until you are mafrish challah from it! Therefore the mishna tells us explicitly that the mitzvah to be mafrish challah applies even in a situation where the whole dough is tamei.
The custom that women developed not to declare the kedushas challah is based on the assumption that if one has in mind that something should become teruma or challah it will only have a lower level of kedushas terumah. The full kedushas terumah will only take effect if one will make a declaration, "harei zeh teruma". Since for the purpose of removing the issur tevel it is sufficient to have in mind that this should become challah or teruma, it is really not permissible to declare that it should become challah because one would be unnecessarily adding an additional degree of kedusha to dough which is tamei. This was the Netziv's justification of the minhag of women for so many years to not declare the challah but rather to rely on the fact that they had in mind that it should become challah.