גְּאֻלָּה (geullah) is the noun derived from גָּאַל (gaal, H1350) — to act as kinsman-redeemer. Where gaal is the verb (the action of redeeming), geullah is either the act itself or the right to redeem: 'the right of redemption,' 'the redemption transaction,' or 'what was redeemed.'
The background is the Israelite property and family law of Leviticus 25: if a person fell into poverty and had to sell their land or themselves into debt-servitude, the nearest kinsman (the goel) had both the right and the obligation to buy the property back or redeem the person. This is not charity — it is a legal right and duty rooted in kinship. The geullah is the transaction by which the kinsman exercises that right.
The Book of Ruth is the fullest narrative exploration of geullah in the OT. Boaz, as a near-kinsman to Naomi's family, exercises the geullah right over the land of Elimelech — and as part of the same redemption package, he also takes Ruth as his wife. The entire book turns on whether someone will step forward to exercise geullah, and Boaz does so at personal cost and as an act of hesed (covenant loyalty).
Theologically, geullah is how the OT portrays YHWH's relationship to Israel: he is the goel, and his redemptive acts — the Exodus most prominently — are geullah. God acts as the divine kinsman who exercises the right of redemption for his people.