What does assigning the copyright of a paper mean?

I have been reading that a publisher called WIT Press has the following copyright agreement:

http://ift.tt/1Dd5MyP

It has one part that says:

We will not withhold permission for any reasonable request from you to publish parts of this paper in connection with any other work by you, provided the usual acknowledgements are given regarding copyright notice and reference to the original publication.

What does it really mean? It means that if a paper submitted to that publisher gets accepted I cannot put it on my personal webpage or in the repository of the university that I am?