A flat-signed book has the author's signature alone, with no inscription or dedication, usually on the title page. Dealers use the phrase to make clear that nothing else is written and no recipient is named.
How to spot it
The signature typically sits on the title page under the printed author's name, sometimes on the half-title or a front endpaper. Look for a real ink signature, not a printed facsimile: real ink sits on the surface and can show pressure, while a printed one is flat and even. A signature on a separate bookplate or tipped-in leaf is described separately.
What it does to value
Many collectors prefer flat-signed copies to inscribed ones, because the book is not personalised to someone else. A flat signature on a first edition usually adds a premium over an unsigned copy, and the premium is largest for authors who signed rarely or died before becoming famous. For authors who signed thousands of copies at events, the premium is smaller.
Read signed and inscribed books for how signatures are verified and valued.