Firstly, read the Wikipedia article that explains UTC/GMT.
Time stamps with time zones are expressed as a date, a local time (eg: 08:00:00, which is 8am), and an offset (eg: -8, which would be 8 hours behind UTC). To convert a local time into UTC you use the offset.
So, in your example of:
TIMESTAMP '1999-04-15 8:00:00 -8:00'
... the local time is 08:00:00, which is 16:00:00 UTC (08:00:00 + 8 hours, because it is 8 hours behind UTC).
TIMESTAMP '1999-04-15 11:00:00 -5:00'
... the local time is 11:00:00, which is 16:00:00 UTC (11:00:00 + 5 hours, because it is 5 hours behind UTC).
The two times and dates in your example are identical when converted to UTC - that is what the sentence in your question means.