What does "Tax Basis" mean?

Haven't read Rosenbaum and this is very little context, but this is most likely what you are looking for:

You have financial/accounting and fiscal book value of assets. Some assets have a different depreciation schedule on the financial balance sheet (where you want to present high profits) than on the fiscal balance sheet (where you want to have high depreciation resulting in low profits resulting in low taxes). The difference between the tax paid (based on fiscal balance sheet) and tax due based on financial/accounting balance sheet is called deferred tax liability (or asset when its the other way around).

When you sell you business in an asset deal, the buyer will have to revalue all assets to the fair market value, resulting in a high tax basis. From there it can depreciate all of those assets again resulting in lower fiscal taxable profits in the following years. However the seller has made a taxable profit on the sale of those assets (fair market value minus fiscal book value). So his loss is the buyer's gain (in absence of timing effects).

In a share deal you just continue with the fiscal book value of all assets at the level of the target.

In some countries you can however offset losses from previous years with the gain of the asset sale, making it more interesting selling (part of) the business by means of an asset sale.