A pattern is an idea, a concept or a model. The model is usually abstract, and can then be applied to the domain where it is used. Pattern matching is checking if a certain pattern is present. Many patterns can directly be recognised by the senses.
Some patterns are based on the fact that there are repetitions, that a certain thing occurs over and over again. An example of a simple pattern might be the tiling of a floor. For example, lots of bathrooms have a paisley or floral tiling pattern on the floor. In computer science, design patterns are model solutions for problems that occur often. Sometimes people see patterns when there are none. This is called pareidolia.
Mathematical patterns change
1, 2, 4, 8, 16, ...
In this pattern, the next number is the product of the previous number multiplied by 2. Basically a mathematical pattern is a sequence of numbers which follows one rule.