A Conceptual Model is a simplified explanation of how something works. by applying a familiar analogy(s) or system to a new system . Strong conceptual models aid users in forming a “coherent image” of how a system work, by allowing them to anticipate potential actions. By borrowing from system that users are already familiar with as a design strategy we promote learning as opposed to memorization. Norman (a professor Hayes) uses the conceptual model of files and folders that we see on most all computers.
Example from Design of Everyday Things: The File Folder system on Computers.
Example from the Web: Trello uses Conceptual model of a Kanban board with post-it notes. You can do just about everything one would do with a physical board.
Example from my Life: I’m going to recycle an item I shared in my histories post, this remote light switch looks and acts wall-mounted switches. Thought it is a different kind of switch, conceptually it is modeled after light switches I am familiar with.
Norman, Don. The design of everyday things. New York: Basic Books, 2013.
Along similar lines, the project management software Asana provides nice examples of conceptual modeling, specifically the analogies of checklists and sticky notes (you can “stick” and move around tasks by dragging): https://drive.google.com/a/uci.edu/file/d/0B_mGausa6-UGbjB1VHlzbk93X28/view?usp=sharing
These are great examples but I would also like to showcase or present another design idea that represents the conceptual model from an object and not necessarily from a software/website like you have shown above.
http://sites.uci.edu/in4matx282f17/files/2017/10/bowl.jpg