Accrued interest (if any) is factored into the price

The price is either dirty or the security is in default or soon to be defaulted. I.e. on fill there will be no separate accrued interest amount. This is often called a flat price.

The effect of bond amortization or the floating rate index offset is factored into the price

The security's price includes the effect of bond amortization or a floating rate index. For example this qualifier would apply to the normal pricing of index-linked UK gilt bonds but not to US or EU index-linked bonds.