From a client’s perspective, an interior design concept should be something that the designer presents to give the client an idea what the end result will look and feel like. Often, this is done through something called moodboard, which is a collection of key furniture, colors, accents, accessories, etc. which will give a rough idea as to what the space would look like after the interior design work is completed.
An interior design concept is the initial blueprint of a design without the numerical specifics. It can be based upon an idea or a peg. Like planning events, the concept can be a theme. For a more opulent feel, the novel The Great Gatsby can be the starting point of an interior design concept. For the more water inclined, nautical can be the jump off point.
The most important thing about an interior design concept is that it is easily communicated to the client in a way that all parties understand it cohesively and that the concept is viable given all other factors such as project timelines and budget.
For a client, a design concept normally could be more of a visual entity that communicates on behalf of the designer. As many other people have already pointed out here, design concepts often take form of a “Mood-board” that can help a client visualize the space before it has been physically realized. A mood-board essentially is a palette of space-making elements such as furniture, furnishing, art pieces, etc. alongside aspects like colors & textures, materials, design language & style, etc. Depending upon the conciseness of the mood-board, it could be a very effective method to communicate your ideas to the client. It could be as simple as a mood-board of a space that is “Minimal, Clean and Crisp”.
Alternatively, for a client, a design concept could also bluntly mean – a theme. A theme is largely visual, and its foundation lies mostly in the visual treatment of a space. Hence for instance, when someone says they have got their restaurant designed with an Arabic theme, you can surely expect to see a lot of intricate geometric patterns and meticulous carvings all over the place. You can make that connection because you can automatically associate both the entities (Arabic with geometric forms & meticulousness) together based on your own knowledge and previous exposure to Arabic patterns & motifs.