How are immersions defined in $PL$-cathegory? For embedding i found the following definition: $f$ is an embedding if it is $PL$ between polihedra and a $PL$-homeomorphism on its image. What does immersion mean in this context? And what's the difference?
Is it correct to say that an immersion is a $PL$ map which is locally an embedding?
Not quite (what is your source?): You also want $f$ to be locally flat. Here is an example to think about: Take a nontrivial polygonal knot $K$ in $R^3$, a point $p$ in the upper half-space $R^4_+$ and consider the cone $C$ from $p$ over $K$. Then $C$ defines an injective PL map of the 2-disk to $R^4$. However, this map is not an immersion (also, not an embedding). See this "Manifolds Atlas" article for the details.