Jivan-mukta means that even though one is in the material body (there are still some material necessities, since the body is material), because one is fully situated in the service of the Lord, he should be understood to be liberated
SB Canto 3
The Personality of Godhead said: My dear mother, the path of self-realization which I have already instructed to you is very easy. You can execute this system without difficulty, and by following it you shall very soon be liberated, even within your present body.
Devotional service is so perfect that simply by following the rules and regulations and executing them under the direction of the spiritual master, one is liberated, as it is said herein, from the clutches of māyā, even in this body. In other yogic processes, or in empiric philosophical speculation, one is never certain whether or not he is at the perfectional stage. But in the discharge of devotional service, if one has unflinching faith in the instruction of the bona fide spiritual master and follows the rules and regulations, he is sure to be liberated, even within this present body. Śrīla Rūpa Gosvāmī, in the Bhakti-rasāmṛta-sindhu, has also confirmed this. Īhā yasya harer dāsye: regardless of where he is situated, anyone whose only aim is to serve the Supreme Lord under the direction of the spiritual master is called jīvan-mukta, or one who is liberated even with his material body. Sometimes doubts arise in the minds of neophytes about whether or not the spiritual master is liberated, and sometimes neophytes are doubtful about the bodily affairs of the spiritual master. The point of liberation, however, is not to see the bodily symptoms of the spiritual master. One has to see the spiritual symptoms of the spiritual master. Jīvan-mukta means that even though one is in the material body (there are still some material necessities, since the body is material), because one is fully situated in the service of the Lord, he should be understood to be liberated.
Liberation entails being situated in one's own position. That is the definition in the Śrīmad-Bhāgavatam: muktir. .. svarūpeṇa vyavasthitiḥ (SB 2.10.6). The svarūpa, or actual identity of the living entity, is described by Lord Caitanya. Jīvera 'svarūpa' haya-kṛṣṇera 'nitya-dāsa': (CC Madhya 20.108) the real identity of the living entity is that he is eternally a servitor of the Supreme Lord. If someone is one-hundred-percent engaged in the service of the Lord, he is to be understood as liberated. One must understand whether or not he is liberated by his activities in devotional service, not by other symptoms.