What EPS is
EPS (Encapsulated PostScript) is an older but still common print format. Printing presses, sign and banner makers, newspapers and some design and layout programs ask for artwork as EPS files, often out of habit or because of older equipment.
What happens when you convert
Each PDF page is drawn at the DPI you choose and stored inside its own EPS file as a high-quality JPEG picture, with the picture's size recorded in the file header. Multi-page PDFs give one EPS per page, downloaded together in a ZIP, or one by one from the file list.
Raster EPS versus vector EPS
The EPS files from this tool contain a picture of the page (raster), not editable vector shapes. They print well at 300 DPI at the original size, but text and lines cannot be edited in Illustrator or CorelDRAW and will not stay perfectly sharp if the artwork is enlarged a lot. If your PDF came from a design program, the PDF itself usually keeps the vectors and is the better file to send.
Common problems and how to fix them
The printer says the file is not editable: ask whether they can work directly from the PDF. The print looks soft: convert again at 300 DPI. Colours look different: the EPS is RGB; printers working in CMYK convert colours, so ask for a proof.
Good habits
Ask the print shop which format and resolution they really need, keep your original PDF, and request a test print for important jobs.