Short answer: The allowed amount (or allowable charge) is the maximum your plan will recognize for a covered service. Your coinsurance is calculated on it, and in-network providers can’t bill you above it; out-of-network providers sometimes can.
The ‘allowed amount’ is the negotiated or plan-set price for a covered service, and it’s the basis for how cost-sharing is calculated; your coinsurance is a percentage of the allowed amount, not the provider’s sticker price. In-network providers agree to accept the allowed amount as payment in full, so they can’t bill you for the difference. Out-of-network providers haven’t agreed to it, so they may ‘balance bill’ you for the gap above the allowed amount (except where the No Surprises Act applies).