Fresh starts are a feature of a test that can make the results more reliable. A test with fresh starts will be divided into a number of sections, each testing a different area of language or skills/subskills, so that no one area dominates. Consider a placement test that includes a speaking test where the learner is asked to talk about what she did for her last holiday and nothing else. Her final mark is liable to be dominated by her accuracy and fluency in using past verb forms, plus her knowledge of the specific lexis involved (eg connected with the sea, mountains, sightseeing or whatever the holiday involved). If the mark is high, it may hide the fact that when talking about the future she relies exclusively on will + infinitive, or if it is low, may not reveal that in general social conversation on other topics, she is both accurate and fluent and has a wider range of vocabulary.
On the other hand, a speaking test which started by asking her to talk about herself (where she's from, family, work, interests etc), then asked her to talk about what she did for her last holiday, and then asked her to talk about her plans for the next few months, would have a number of "fresh starts" - ie changes from one topic and area of language to another. If she showed weakness in the "holiday" section this time, but performed accurately and fluently in the others, her final mark would be much more representative of her overall competence.
So fresh starts lead to a much more reliable result - there is no chance of the result being swayed by a specific strength or weakness.