What does an embedding over $K$ mean?

Question

I have some understanding problem. In the topic of extensions they always speak about embeddings over some field $K$ and i have absolutly no idea what this means. One example is the following:

Let $K$ be an algebraic extension of $k$ contained in an algebraic closure $k^a$ of $k$. Then the following statements are equivalent:

1. Every embedding of $K$ in $k^a$ over $k$ induces an automorphism of K
2. ...
3. ...

So but what does this exaclty mean? from where to where does the embedding goes?

Another example is the following.

Assume that $K\supset E\supset k$ and that $K$ is normal over $k$. Let $\sigma$ be an embedding of $K$ over $E$...

What does this mean in this case?

Thanks for your help because I'm really confused with the formualtion and it's meaning