Pronouncements sounds very similar to announcements (which means to declare something). Pronouncements actually means a formal or authoritative declaration. Therefore, pronouncements in sciences would refer to any evidence or findings that have been obtained as a result of studies and researches which have been declared authoritatively.
In the second part of the statement, Sir James Jeans tries to convey the message that many scientific pronouncements have been proven wrong.
The most famous biomedical pronouncement that was proven to be false was the link made between MMR vaccines and autism by Andrew Wakefield. This link was later debunked by science as no research or study could prove that MMR vaccines were linked with autism. This pronouncement, however, caused lots of parents to refuse the MMR vaccination for their children. This resulted in many deaths due to measles, mumps and rubella.
This case highlights the importance of taking precautions before making an official biomedical pronouncement.
Others may argue that without pronouncements, we would not have the technology that we have now. Take the case of Dr. Edward Jenner, the father of immunology.
His research involved exposing people to cowpox (which was harmless) to immunise them against smallpox. If Dr. Edward Jenner had not pronounced his findings and evidence, our knowledge of vaccines would not be possible. Similarly, Sir Alexander Fleming would not have discovered antibiotics.
Making pronouncements may motivate other scientists and doctors to follow in the footsteps of the likes of Dr. Edward Jenner and Sir Alexander Fleming.