Basics first. The definition of concatenation says
$R \cdot A = \{ab | a \in R \ and \ b \in A\}$
Now, if $A = \phi$, we can never form a string $ab | a \in R \ and \ b \in A$ since no matter what we do, second condition will always be false. Thus $R \cdot \phi = \phi$
Next, Kleene star definition says
$R^* = \{\epsilon\} \cup R^1 \cup R^2 \cdots$
Where $R^i$ is $i \ times$ concatenation of $R$
When $R = \phi$ for $\forall i \geqslant 1, R^i = \phi$. Thus $R^* = \epsilon$