Short answers, pulled from the story.
Saṅkhāra is a Pali term meaning 'formations' or 'that which has been put together' and 'that which puts together.' It carries two senses: in the passive sense it refers to conditioned phenomena and mental dispositions; in the active sense it refers to volitional karma that drives dependent origination and rebirth.
According to the Mahāparinibbāna Sutta, the last words of the Buddha were: 'Disciples, this I declare to you: All conditioned things are subject to disintegration, strive on untiringly for your liberation.' The word for 'conditioned things' in the original Pali is saṅkhāra.
The Sanskrit equivalent is saṃskāra, a cognate term that appears in the Kaushitaki Upanishad (verse 2.6), the Chandogya Upanishad (verses 4.16.2-4), and the Brihadaranyaka Upanishad (6.3.1), among other classical and epic era texts. It is not a Vedic Sanskrit term.
The cessation of sankharas in their active, karma-generating sense is described as synonymous with awakening (bodhi) and the attainment of nirvana. However, even in a liberated being (an arahant), the karmically-resultant-consciousness (vipāka viññāna) continues to exist during their lifetime as a residue of past karma.
Saṅkhāra fuses object and subject as interdependent parts of consciousness with no single-word English equivalent. Translators have used 'formations,' 'fabrications,' 'concoctions,' 'determinations,' 'constructions,' and 'preparations,' each capturing a different facet; Bhikkhu Bodhi himself uses two different renderings depending on context.
In dependent origination, volitional formations (sankharas) arise from ignorance (avijja) about impermanence and non-self. Those formations condition consciousness, which in turn conditions renewed becoming, future birth, aging, death, and the full mass of suffering. Breaking this chain at the level of sankharas is what liberation entails.