Short answers, pulled from the story.
The five skandhas are form (rupa), sensation (vedana), perception (samjna), mental formations (samskara), and consciousness (vijnana). Together they describe the material and mental factors that take part in the perpetual process of craving, clinging, and aversion arising from ignorance.
Skandha means multitude, quantity, or aggregate in Sanskrit, generally in the context of a body, trunk, stem, or anything of bulk that can be verified with the senses. The Pali equivalent khandha means bulk of the body, aggregate, heap, or material collected into bulk.
The skandha doctrine asserts that everything perceived, including every person and personality, is an aggregate of composite entities without essence. All Buddhist traditions hold that the aggregates do not constitute a self, and realizing their impermanent, non-self nature is considered necessary for achieving nirvana.
The Heart Sutra, whose Sanskrit title is Prajnaparamita Hridaya Sutra, states that the five skandhas are empty of self-existence. It contains the declaration that form is emptiness and emptiness is form, extending the same logic to feelings, perceptions, mental formations, and consciousness.
In classical Buddhist doctrine, dukkha, meaning unease or suffering, arises when one identifies with or clings to the aggregates. Each aggregate is described as an object of grasping at the root of self-identification, and suffering is extinguished by relinquishing attachments to them.
Nagarjuna was the author of the Mulamadhyamakakarika, the foundational text of the Madhyamaka school. He refuted the Sarvastivada conception of reality, which treated phenomena as real, and argued that the skandhas too lack substantial existence because they are dependently originated.