You'll see this phrase all over the Internet when searching for Web site development. The term "custom" web design has itself become incredibly diluted in its meaning. Advertising can quickly gloss over a true meaning of a word by hoping that its target audience doesn't fully understand the term's definition, or the context of the term.
Most of the time the term "Custom Web Design" means using design templates that you can "customize" - which is different than an actual custom design that is started from scratch. Sure, you can change pictures in pre-coded spots, maybe change colors and positions, but in the end the design is a prefab template - this is NOT custom design, it is customized design.
Be aware that there could be dozens or hundreds of other companies using the SAME template that you're using, which in the end, could well damage your image and not promote it.
For those who create a definitive custom design, their web design process starts with a blank page and a strong connection with the client's vision and needs. The goal of the custom web designer is to create a unique, one-off design that will stand out from template designs that do not satisfy or adhere to the needs of design conventions, nor capture the client's perspective.
If you are looking for a custom web site design, make sure you are getting a unique design by asking your web designer if the design is based on a template or if they build from scratch. Take a look through their portfolio and see if their work shows variety, improvisation and innovation while providing proper navigation and content flow.