“Āvyo śaraṇe tamārī” (Gujarati: આવ્યો શરણે તમારી) means “I have come into Your refuge.”

• In Jain bhakti, this line is a humble prayer to the Jin (Arihant Tirthankars) and to the Jain śāsan, expressing surrender, asking for guidance to walk on samyak darshan–jnān–chāritra, and for strength to reduce kāshay (anger, pride, deceit, greed).
• It is a devotional phrase (stavan/bhāvnā line), not a canonical sūtra. Both Śvetāmbara and Digambara traditions use such refuge-seeking language in prayers; there is no doctrinal difference in its basic meaning.
• You may hear similar lines in many Jain stavans where the devotee says, “I have come to Your śaraṇ (refuge), please accept my bhakti and guide me toward moksha.”

For a short explanation of “śaraṇ” (refuge) in Jainism, see this reference: Example of a stavan where the wording “aavyo śaraṇe” appears: