The best procedure is to NEVER embed an image in InDesign. By default images are linked when you place them, and they should stay linked, not embedded. This keeps the file size down and makes work more efficient, and allows you to update the image.

Then use the PDF/X-1a:2001 preset when exporting your PDF.

What does PDF/X-1a have to do with images in the PDF file? If you mean embedding fonts, most of the PDF export settings of InDesign by default embed all fonts. And if you want to go the route of PDF/X, we at Adobe most strongly recommend PDF/X-4 given that it provides for live transparency and color management in the resultant PDF file yielding a much more reliable and flexible workflow. (PDF/X-1a yields PDF with device-resolution and device-color space dependent output including flattened transparency!)

          - Dov

Since there is no such thing as “embedding layers” either in InDesign or in PDF, either you misunderstood what the printer was telling you, the printer made a gaffe in telling you “layers” as opposed to something else (possibly “images”), or unfortunately, the printer doesn't know his *ss from his elbow.

Given that the issue was related to images, I suspect the printer was trying to tell you to embed the images in the InDesign document (as opposed to placing them via links) as a way of making sure that when the PDF was created, the full image, and not some low resolution proxy, was being exported.

That having been said, without seeing your original InDesign document and the resultant PDF file, it is virtually impossible to further second guess what was going on. What we can tell you is that (1) there is no such thing as “embedding layers” and (2) embedding images as opposed to placing with links is not best workflow practice.

          - Dov