Below is a paragraph - from a known book -
which I have difficulties understanding. Please
somebody explain in more clear terms the
phenomenon.

the context was about dipole antennas,
however the comment has a general nature

"Radiation of electromagnetic waves is created
when the alternating electric and magnetic fields
attempt to collapse back toward the antenna.
However, new fields being created by the next
half cycle push the preceding fields into space,
which is the mechanism of radiation."

- from "The Beginner's Handbook of Amateur
Radio" by Clay Laster, page 260

Cordially,

Nic. Santean
http://www.csd.uwo.ca/~nic/