"Manual tax" is where the tax amount has been manually edited on an order to override the amount which was calculated using the applied tax code.
This might be required to resolve rounding differences between Brightpearl and another system. For example, a purchase order created in Brightpearl might have a different tax amount than on the invoice received from the supplier even if the product prices and tax rates all match. In this case the tax amount can simply be retyped to match the supplier invoice so that the invoice can be received against the order.
Alternatively, an order downloaded from a sales channel may have a different tax amount from that expected by Brightpearl using the given tax code.
You can tell that manual tax has been applied on an order because the tax amount against a line item will be in a yellow box instead of the usual white.
Note that changing an item quantity or discount on a line normally recalculates the line price and tax, but if manual tax is set, the tax amount is not updated.