To know how your thoughts can change the word, you need to know what thought is. Thoughts are things but they exist as unmanifested matter with pure potentiality (infinite possibility and creativity). The main difference between thoughts and manifested things is the hierarchical change in frequency of the consciousness of the observer (you).
Thought, matter, and the external reality
Thought is an attribute of consciousness that acts like a focusing and filtering system. One of the main roles of thought is to focus everything in the external world into holograms, which are thought projections. A hologram is similar to an image but is three dimensional and multidimensional in nature. Within any point on a holographic image, no matter how small, all knowledge of the whole image is present.
Everything in the Cosmos is focused into existence by the thought of the Prime Creator. In other words, reality is thought construction. If the Prime Creator ever loses Its mental focus, every object in the Universe would simply vanish into thin air. Once you comprehend this knowledge, you should know that the reality you live in behaves more like an illusion.
Our version of reality works very much like an illusion, because when we break matter down to its fundamentals, it is mostly empty space and is made of only energy. One important thing you should know about the external reality is that the farther you move away from the Source that manifested the external reality, the less energy it can hold and thus reality becomes more and more like an illusion.
For strong evidence that the material world works like an illusion, read my empowering article titled What is Reality? How It Relates to Your Well-Being.
Thought has infinite potentiality
Thought is a subtle energy that influences everything we do, because every action involves the use of thought. Even though it is subtle, thought has infinite potentiality (possibility) and is the most powerful manifestation energy force in the Universe. It is so powerful that it has the power to manifest energy into material things.
Thought is the creative power that the Prime Creator uses to focus everything into being. The pure form of thought has no limitation due to the fact that it has infinite potential. The fact that you have thought is proof that you are a sentient being with infinite potential. However, because you are still in the very early stage of your evolution, you do not have access to the true power of thought.
To gain access to the true power of thought takes time, dedication, hard work, spiritual wisdom, personal responsibility, and eons of life experiences. The main reason for these requirements is because the true power of thought is too powerful for a naive human being to play around with.
Allowing a naive human being access to the true power of thought is like giving a baby fire to play with in a room soaked with gasoline and filled with explosive materials. In other words, if you are given access to the true power of thought without learning how to be a responsible being, you could destroy the Universe. With great powers come great responsibilities.
Once you comprehend and accept that thought is one of the fundamental energies that creates the Cosmos, you should realize that your thoughts can change the world.
Why you need to stop thinking that you are weak and powerless
When you think you are weak and powerless, and believe that you cannot change the world, it affects the collective human consciousness, which is the thought field that creates our reality here on Earth. Your own thoughts only affect this thought field to a small degree. However, if the rest of humanity thinks that they cannot change the world, it affects this thought field to a very large degree, causing psychological problems to manifest throughout the population.