The gemara in Rosh Hashana 9b says that the word is related to דיירא (dwelling place) and means someone who is subject to noone's will but his own. He chooses his own place of residence and will make his living wherever he finds himself. He will refuse to subjugate himself to anyone.
The פני יהושוע points out that the pasuk say לכל ישביה (all its inhabitants). This means that even if a person is a slave owner, he is not considered "free" unless the entire society is free. As long as there are those who are slaves, he himself cannot be considered free. That is why we have the saying
כל הקונה עבד כקונה אדון לעצמו
Whoever purchases a slave, it is as if he has obtained a master for himselfTherefore, it is only when the slaves are set free that we can say that the inhabitants of the land are free.
Rabbi Samson Rafael Hirsch shows the usage of the bird as one that does not allow itself to be tamed but makes its nest in a human house just as if it was an open field or wild forest. It uses the term מרור דרור, pure myrrh. It uses the word as a legal term, דררא דממונה which is explained as a situation that requires a decision of the court even thought he parties involved have not brought the question to the court. He then declares that the basic meaning is "to follow a natural trend". That is, the "dror" is something that follows its intrinsic nature and does not allow itself to be coerced into being "adulterated" in any way.
We see therefore, that the declaration of freedom is not only a responsibility of sending out the slaves into "freedom", but the responsibility of a person to make himself free to follow the nature that Hashem gave him. This is why we regard it as a requirement to serve Hashem. During the Yovel year one cannot continue to be a "slave" to the land but must follow the laws of shmita.