Sorry but I disagree with Phil's explanation. Many companies have a Research and Development (R&D) department that designs new products. They might also have a product engineering department that fixes and improves existing products. For new products, "out the door" means moving a product prototype from R&D or engineering to manufacturing or production. The idea is that, as long a a product is still an R&D or engineering prototype, it is kept (for the most part) inside the company. Once the product is released to manufacturing for production, it is "released" to the public for purchase and so is "out the door". For existing products, the current product version is already "out the door". However, a newer product version that fixes problems in the current version may be developed and tested by the product engineering department. Once the new product version is released to manufacturing and sold/distributed to the public, it is said to be "out the door". In essence, the "door" stands between R&D/product engineering and manufacturing. Hope this explanation helps.

"Out the door" means out of the company's production area and into the marketplace.

The use of "the release" means it's in the software industry to me. So the release means, most lively, make it available to customers however that is done: provide a patch to download, issue a complete new version, etc. it could mean to get it to a QC process, but that seems less likely to me.