In a simple term, geometry is a branch of mathematics that studies the size, shape, and position of 2-dimensional and 3-dimensional figures. And it is also the study of local and global properties of spaces. We developed the concept by studying simple models with concepts of points, lines, shapes, lengths, etc. The idea of space is considered to be a natural concept that comes up when we begin to understand the world.
Next with an excellent idea of using numbers to represent points, people started studying more complicated objects and their properties. The concepts of curvature, topology, and metrics were developed. People began to construct and think about more abstract and interesting spaces by adopting the different ideas of coordinates and more algebraic methods. The idea of the notion of space changed a lot and took several transformations. Understanding the symmetries of space and several classes of functions associated has also become the most important aspect of geometry.
Moreover, abstract structures defined purely algebraically tend to have some local and global aspects which hint at the geometry involved. There are some “geometric” properties that don’t depend on the coordinates or fields, rather show the representations of the objects at hand.
Geometry helps us to identify this equivalence of different representations and provides a more conceptual explanation of mysterious relations.
In short, geometry is fundamentally a way of thinking which allows us to effectively understand the properties of an object/structure we are studying.