The answer to this question varies depending on the Vedanta school.
Advaita Vedanta
This school believes both in moksha while still living (Jivanmukti) or after death (krama-mukti). Essentially the liberated person attains the state of Brahman and does not go to any place.
Yudhisthira on Emancipation
There are two well-known paths (for us), viz, the path of the Pitris
and the path of the gods. They that perform sacrifices go by the
Pitri-path, while they that are for salvation, go by the god-path. By
penances, by Brahmacharya, by study (of the Vedas), the great Rishis,
casting off their bodies, proceed to regions that are above the power
of death. Worldly enjoyments have been styled as bonds. They have also
been called action. Liberated from these two sins (viz, bonds and
action) one attains to the highest end. ….As a person on the hill-top
looketh down upon men on the plain below, so he that has got up on the
top of the mansion of knowledge, seeth people grieving for things that
do not call for grief. He, however, that is of foolish understanding,
does not see this. He who, casting his eyes on visible things, really
seeth them, is said to have eyes and understanding. The faculty called
understanding is so called because of the knowledge and comprehension
it gives of unknown and incomprehensible things. He who is acquainted
with the words of persons that are learned, that are of cleansed
souls, and that have attained to a state of Brahma, succeeds in
obtaining great honours. When one seeth creatures of infinite
diversity to be all one and the same to be but diversified emanations
from the same essence, one is then said to have attained Brahma. Those
who reach this high state of culture attain to that supreme and
blissful end, and not they who are without knowledge, or they who are
of little and narrow souls, or they who are bereft of understanding,
or they who are without penances. Indeed, everything rests on the
(cultivated) understanding!’
Mahabharata Santi Parva Section XVII
Other Vedanta school say that the liberated is able to reside with the deity worshipped by him.
Dvaita Vedanta
According to this school moksha is only possible after death. In ascending order, this school believes in four levels of moksha: (1) salokya, (2) samipya, (3) sarupya and (4) sayujya. ….. In salokya mukti, the departed soul goes to Ishta-loka (the abode of Vishnu) and stays there blissfully enjoying His presence. In samipya-mukti the departed soul enjoys the bliss of extreme proximity to Vishnu. In sarupya-mukti the departed soul acquires the form of Vishnu and enjoys intense bliss. In sayujya-mukti the departed soul becomes blissfully absorbed in Vishnu.
Vishistadvaita Vedanta
The school of Qualified Non-dualism or Vishishtadvaita-vada, is a school of theism. Its main exponent was Ramanuja. According to this school, a person can have moksha only after the person’s death. Moksha means living blissfully in Vaikuntha (the abode of Vishnu) in spiritual bodies. They acquire many divine powers such as omniscience, but unlike God they cannot create, sustain, or dissolve the world. In spite of their exalted state they remain subservient to God.
What is the progress in coming from the Supreme abode and then going to that place again after a few births?
The Jiva does not come from the Supreme abode. The Jiva is an emanation of Brahman for the Advaita Vedanta school. Other schools do not say that the Jiva is an emanation of Brahman.
