Here are a few reasons why investors love prototypes:
Creates an emotional connection.
Investors are more likely to put up money if they have an emotional connection to the product, and that's most likely to happen through a prototype. The reason being is people's attitudes about a product change when they take it into their hands and use it. (If people need to rely on their imaginations to understand your product, they're not going to get excited.)
It is expected.
Standards for prototypes have gone up a lot in recent years due to easy and cheap 3D printing, the low cost of building a website and electronics prototyping with development boards. So in most cases a crude mockup or basic proof of principal model is not going to cut it anymore. Investors expect you to utilize these low-cost resources if you want to get their attention.
That said, there are some exceptions to the rule: Friends and family may invest money before seeing a working prototype. Also, teams with exceptional track records can often raise a round with little more than a seed of an idea.
Know where you are in the game.
While having the best possible prototype available during a pitch session is critical, not every startup will be able to create a top-of-the-line one. Refinement is expected but having a prototype helps investors understand where you are in the process.
For example when we started E Ink, the company that makes the electronic paper displays for Kindles and Nooks, the "ink" barely worked.
We couldn't make anything like the display in the current Kindle, and it took years for the technology to get to that point. But we had a compelling story about a world full of people reading electronic books and newspapers instead of pulp and paper publications. This coupled with a proof of principal prototype was enough for investors to connect the dots and see what was possible.
Allows for feedback.
We often work with entrepreneurs who are cycling through the product-development process at the same time they're raising money. We expect them to pause at different phases of the project to complete fundraising rounds or to use the prototype to get customers and companies interested in a more refined version. And with a physical prototype, it is much easier to respond and provide input.
They often come back with essential feedback that informs the next phase of the design process. It's much easier for someone to respond to the physical vs. the abstract.
Exposes weak points.
A prototype can more easily highlight your weaknesses, which could be a good thing, as it helps investors understand what further resources are needed. (And this may deepen the emotional connection - giving feedback can get an investor, well, invested.)