A thinly capitalised entity is an entity funded by a large amount of debt and very little equity. Due to the large amount of debt, there can be potential to claim large tax deductions for interest payments on that debt.
Some foreign-owned entities will attempt to lower their taxes in Australia by creating loans to Australian business and using the interest payable as a deduction. The interest income is then recognised in another tax jurisdiction.
Like transfer pricing, thin capitalisation is closely watched by the ATO to ensure that profits are not shifted away from an Australian entity to another country with lower tax rates.