Any notions of operations in basic postulates of lambda calculus I am learning Lambda Calculus from the book by Hindley and Seldin . They start the formal postulation of lambda calculus as follow : 

(a) all variables and atomic constants are λ-terms (called atoms); 

(b) if M and N are any λ-terms, then (MN) is a λ-term (called an application); 

(c) if M is any λ-term and x is any variable, then (λx.M) is aλ-term (called an abstraction).

In the second postulate $MN$ has been termed as a $\lambda$ term . How to define $MN$ , what does it mean ? Is it an operation?
Is there any scope of defining operations in lambda calculus which are associative and/or distributive  ?
You can think of application $MN$ as an algebraic operation, where the operator has been elided for convenience. Instead of $MN$ some people write $M @ N$, or even
$$
apply(M, N)
$$
So $apply(\cdot, \cdot)$  is a binary operation, and, as @chi points out,
 $apply(\cdot, \cdot)$ is is neither associative nor commutative. The precise nature of what $apply(\cdot, \cdot)$  does depends on exactly what $\lambda$-calculus you have in mind.