Nowadays, there's a lot of enthusiasm both in the corporative spheres as in the innovation centers, universities and smaller companies with regards to the use of design thinking as a method for innovation in products and services. In my experience, there's usually some confusion created when one overemphasizes the given names of things (usually for marketing reasons) and leave somewhat at the background what they actually are and what is the logic and characteristics that allow us to understand them. I was definitely confused when I had just heard about design thinking and it took me a while to clear my mind, that's the expense I want to save you with this post.
We can express this same process in terms of 5 phases:
What's the point of each and every one of these phases? Let's explore them...

Put in simple terms, this phase is all about trying to understand the real, concrete problems of a given group of people connected to the project or business you're pursuing. These problems can be as diverse as the lives of the people who suffer them. For example, if you're trying to understand office workers, daily commuting can be a real pain point; if you're trying to understand remote workers, that problem just doesn't exist (or it exists in a different way, it's a different problem).
This brings us to the importance of not relying fully and blindly on the ideas you already have about the problems of a group of people (for example, you could think the main issue for cyclists are car drivers when in reality their main issue are pedestrians and so on...). In order to truly understand the problems of the group of people you're interested in, you need information; you need to gather reliable quantitative (numbers and measurements) and qualitative data (stories, answers to open questions, ethnographical investigation, and so on).
All the data you gather is not gonna deliver you mechanically the main issues for a group of people, it's only an input that we need in order to "rebuild" the experience of that group of people. The best way to comprehend the problems of a person is to put oneself in his or her place, generate empathy, get into someone else's shoes.
Having gathered all the necessary data and having reasonably understood the situation of the chosen group of people, we need to evaluate which of the problems found are key for those people and which are the ones we can tackle with our project or business.
The outcome of this phase should be a series of questions about the main problems of the chosen group of people (for example, if we now know that a certain neighborhood's main issue is the water supply on the area, we must get to the point of asking how can we solve water shortage in the area).

Now, having a set of clear questions, we can use brainstorming to produce solutions for the problems found. In the first phase the main task was to gather enough data to put oneself in the other person's shoes; in the second one, the main task was to define the main problemas for that group of people. In the third phase, all our energies should be devoted to imagining solutions for those problems. A really important thing is you need to put aside any judgement of the solutions you think of, for as long as the brainstorming lasts:
After the brainstorming is done, you'll be able to judge which solutions are good or realistic. The goal after the brainstorming process is to focus both on the most innovative solutions and the most realistic ones.
Ideally, one should enter the prototyping phase with a couple of ideas (2 or 3 tops). To create a prototype, you should select an idea that requires a small ammount of resources and time in order to be made something concrete. The idea chosen could be a product (like a new type of wallet), a service (a new counseling service for entrepreneurs) or an experience (a new thematic restaurant). The main thing is being able to create detailed and really specific prototypes; our prototypes should give a clear idea of the product, allow a clear comprehension of the service or give a clear impression of the experience wanted.

The main goal of prototyping is to test and the main goal of testing is to reduce risk. How do you reduce risk by testing a prototype? You reduce it by increasing the opportunities of improvement without it being a costly task. Let me put it in another way: What happens if I take a loan with my house as collateral, start my dreamed business, create a hell of a product that all my friends like, try to sell it in the market and nobody gives 2 cents about what I have to offer? Sounds like a high risk right?
What we want to do, then, is to create a small, simple, less costly version of our product, service or experience and gather feedback from our potential customers. If this first version sucks, people will tell us why they hate it and we will be able to transform it or, in the worst case scenario, drop it and move on. If our prototype works, people will tell us what else they need and we will be able to improve it. Last but not least, if people really, really love our prototype, we'll be able to party and take vacations!
You may have also noticed that this is an endless process: one can be constantly exploring problems, better defining them, searching for solutions, generating prototypes and testing them. Imagine what would happen if each and every organization you come into contact with on a daily basis (your employer, your university or institute, your company, and so on) applied this approach in a permanent manner in order to develop products, services and experiences. In fact, you could actually apply this same approach to your daily life (to your habits, office work, to your own business, and so on).