Oh, right first, let me explain what is design. Design is a discipline of solving human problems through non-linear ways. Problems are solved through artifacts, physical or abstracts.
To be a designer you need to understand how humans interact with one another and with their environment. Designers use visual and physical tools (software, drawings on paper, physical objects, models, prototypes) to communicate an idea to a builder (it could be an electrical engineer or in Hopscotch case, a software engineer) so they could make it.
To be a designer you need to be educated in things such as history of art, engineering, design theory, and the specific discipline you're working on (fashion, graphics, architecture, software). A designer is the intersection of a scientist and an artist. But while art is about expressing yourself however you want, design is about solving problems and creating "things" to help people. To transfer information (graphic design), to inhabit a space (architecture), to protect you from the weather (fashion design), to help you make complex tasks(interface design), to help you have a more comfortable life (industrial design).
In my case, I design Hopscotch interfaces. With my team, I draw options of screens and the flow of how the app is going to be used. Then we can discussed them, and engineers and other designers and very very smart people in my team can decide what's better for our users. My job is to facilitate "ideas" through visual communications and other interactive tools. If someone says "it will be cool if we can have user accounts, so you can make log-in and log-out", then, the next question will be "Ok, cool, but how does that look like? How will that work?". My job is to translate that idea from imagination to drawings and designs with colors, measures, dimensions, buttons, so everyone can see the implications. Sometimes challenges are more technical, sometimes they're to make Hopscotch a more delightful experience. What do I do at Hopscotch? For example, I drew the new Avatars. But also I draw a lot of the iconography and the dimensions for every screen.