Tapasya (austerities) in Jainism means disciplined self-control, penance, and voluntary hardship aimed at purifying the soul and reducing the influx of karmic matter. Here is the simple, core idea:

• Why karma sticks to the soul: Karmas are subtle substances that attach to the jiva due to passions (kaşāyās), wrong beliefs, and actions. They bind the soul and cause bondage and rebirth.
• How tapasya helps: By restraining passions, mind, speech, and body—through fasting, controlled senses, celibacy, truthfulness, and other austerities—the seeker diminishes the causes that attract new karmas and weakens the existing karmic attachments. Over time, this purification burns off or neutralizes many karmic particles.
• The result: Less future bondage and gradual cleansing of accumulated karmas. With persistent and correct tapasya, the soul progresses toward kevali (omniscience) or, in practice for most, toward moksha (liberation) by erasing the seeds of karma and preventing new seeds from forming.
• Important nuance between traditions:

- Digambaras emphasize more severe, ascetic practice as central to shedding karma. - Shvetambaras emphasize a path that blends strict vows with a household or lay life, focusing on samvara (restraining) and nishkama pratikraman (self-purification) to gradually purify karma.

• Practical takeaway: Tapasya is not just outward hardship; it is inner transformation—cultivating right faith, right knowledge, and right conduct to uproot passions and stop new karmic influx.

If you’d like, I can share a concise outline of specific Jain sutras or stotras that describe tapasya and its effect on karma, along with the traditional meanings (including differences between Digambar and Shvetambar interpretations).