What is textile converter?

Someone who takes greige fabric and makes finished product is the general definition. It can also be made more specific by the person using the word since it can mean different things to different people.

From the reference:

CONVERTER: An individual or organization which buys greige fabrics and sells them as a finished product to cutters, wholesalers, retailers, and others. The converter arranges for the finishing of the fabric, namely bleaching, mercerizing, dyeing, printing, etc., to the buyers’ specifications.

Dyeing Printing Finishing of Textiles Apparel and Home Fashions

A textile converter converts greige (unprepped) fabric into a finished cuttable product to be sold to garment manufacturers, retailers, jobbers, wholesalers, etc. Textile converters must often coordinate the sourcing, prepping, and printing or dyeing of fabric.