When we say xH = Hx where H is a normal subgroup of G and x is an element of G, what exactly does that mean? If y is an element of xH, what do we know about y? If y is also an element of Hx, what do...

When we say xH = Hx where H is a normal subgroup of G and x is an element of G, what exactly does that mean?

If y is an element of xH, what do we know about y?

If y is also an element of Hx, what do we know about y?

How are these two “facts” linked together by the “=”?