To "play safe" is just not to take risks. In the context of a language examination, this might mean not attempting to use sentence constructions that you're not 100% certain of, because of the risks involved.
Therefore an alternative way to express this sentence might be "It can often be better to keep things simple in exams than to be original"
Adding to the explanations above, I think this is very sound advice.
Your purpose in the exam is to pass, not to change the world - leave that for tomorrow
You should know what is expected of you to pass.
In a history exam, you will know how the course was taught, you may well know the views of the examiner. You may have original views on the questions in the exam, but if you know that these would be considered juvenile fantasies by the examiner, you would be better to play safe and either pick another question or present the answer most likely to meet with the examiners approval.
So, in an English exam, although you are totally convinced that the future lies in the overwhelming dominance of textspeak abbreviations, you would be well advised to play safe and write in conventional language.
In the English-Only forum we often talk about the way English is used flexibly and the supposed rules that are not always followed. There is often a comment along the lines of, "This is the way XXXXX is now used in most normal situations, but students of English should be aware that it may not be acceptable in exams or course work". In other words, they should play safe.