A feature is a piece of information in an image that is relevant to solving a certain problem. It could be something as simple as a single pixel value, or more complex like edges, corners, and shapes. You can combine multiple simple features into a complex feature.
Applying certain operations to an image produces information that could be considered a feature as well. Computer vision and image processing have a large collection of useful features and feature-extracting operations.
Basically, any inherent or derived property of an image could be used as a feature to solve tasks.