Lambda Expressions were introduced to Java in Java SE 8. These expressions are modeled on the basis of the mathematical concept of Lambda Calculus (also written as λ-calculus).
There are two concepts from λ-calculus that are worth mentioning here:
Using the above two principles, Lambda expressions in Java provide a clear and concise way (aka anonymous) to represent one method interface (aka functions of a single input) using an expression.
E.g. the mathematical function f(x) = x + 2
In Lambda Calculus: λx.x+2
In Java: (int x) -> (x + 2)
As you may notice, lambda expressions in Java are written in the format: (Argument List) Arrow Token (Body)
Here is another example where an anonymous function receives two inputs x and y and returns their sum: (int x, int y) -> (x + y)
Now although the examples above do not show a return statement, you may very well write multiple lines in your Body and return an appropriate result.
The one method interface in Java is called a Functional Interface. Lambda expressions provide an elegant way to implement such one method interfaces.