Modeling potential implementations. To abstract is to condense a larger object to its essential parts ignoring details. When we write a paper we might write a brief summary or abstract to let the reader know if they want to read the whole paper. For example two implementations of a linear list are an array or a linked list. The abstraction for both of them is the same.
Mathematics have many abstractions including the seven postulates of Euclidean geometry.
For example a string composed of a name might have a selector to pull out the first name. For integers we might multiply. High level languages were developed to help programmers to solve problems correctly. Structuring the data - all data is structured in some way. Then each data type is recognized not only by its data items but by the operations associated with it.