The relative importance of predicted grades will vary depending on the university and your course.
In the UK, they are considered quite important, so it is in your best interest to achieve a good predicted score. Some universities will offer lower conditional offers, unconditional offers or additional scholarships to entice students with higher predicted scores. This means you should study hard for your summer assessments and work towards achieving a good coursework grade to improve your chances. For courses such as medicine or law, where there are standardized tests, universities will often rely more heavily on your performance on these tests as a means of comparing you to your peers. Universities may also place emphasis on your GCSE grades.
In the US, predicted grades matter less than in the UK because they accepted you based on a holistic admissions approach. They consider your standardized test scores, essays, extracurriculars, teacher recommendations, and interviews. Most American high-schoolers actually don’t do the IB – APs are more common! That said, if your scores significantly drop (i.e. you achieve several points lower than your predicted), some US universities may rescind your offer, notify you about their concern, or urge you to take a gap year. This is unlikely, but you should do your best to achieve (or exceed) your predicted grades because universities expect the same level of achievement from you as when they accepted you. Good IB scores may even make you eligible for certain programmes and scholarships, or earn you college credit!