How many stitches are in an embroidery design
The stitch count measures the machine work: more stitches mean more running time and more thread. It also drives the price of the file and of the embroidery.
What increases the stitch count
Filled area matters most: a fully colored crest has far more stitches than an outline of the same size. Then comes size (doubling the width nearly quadruples the area) and stitch type: fill uses more than satin, which uses more than running stitch.
More stitches is not more quality
Too much density makes the embroidery stiff, puckers the fabric and breaks needles. A well digitized file uses the fewest stitches that cover well, with underlay to support them. That is why two files of the same logo can have very different stitch counts and opposite results.
How to reduce it without losing quality
Simplify details that do not show at the real size, swap large fill areas for an outline or a more open texture, and reduce the size a little. Ask for a suggestion together with your quote.