SATs results aren't at all important to children, although handled properly they can help by teaching children the benefits of preparing for exams and by encouraging independent, focussed work. Handled badly, they can do the exact opposite.
However, they are immensely important for schools. Every autumn we receive huge amounts of data based on our valued added scores (measures of individual children's progress from Year 2 to Year 6), compared with schools nationally and county wide. They also compare them with schools with similar entitlement to free school meals, and are broken down between girls and boys. Page after page of data, graphs, analysis and comparisons.
Head teachers are assessed on their results, as are teachers, as their pupils' value added goes towards their performance management and therefore their eligibility for higher salaries once they reach the top of the pay scale. Poor SATs results can trigger an OFSTED or mean that your school is targeted by the LEA and inspected and action planned endlessly. Schools are basically categorised as highly effective, effective or failing, depending on their results, and it doesn't matter how fabulous the ethos of the school is, how much support you have from parents or how creative and enjoyable the children's education is, schools, teachers, governors and Heads will still be judged by their SATs results. Not to mention league tables. It all ultimately affects how much power a Head has to run his/her own school. If you are 'failing', your school will effectively be taken over by the LEA. It happened to ours in the 90s, and I'm so glad we've pulled through it.
Incidentally, categorisation can be skewed by three things, which schools battle constantly to overcome. 1) If a child is absent for whatever reason - illness, bereavement, holiday - on the day of the test, they are still included. At our school last year, we had one parent who took their child out of school for the week, and another whose mother died the day before SATs started. Their results were still included, and resulted in our categorisation going down. 2) If you have children who are entitled to free school meals, but whose parents, quite reasonably, don't want to declare their personal circumstances to school, then you will be placed in a higher band and be judged against higher criteria. We currently have 7.6% entitlement, and are presently categorised as C (just about effective). If all our entitlements were claimed, we would be in the next band and would probably be a A or B school. 3) You are penalised if you welcome special needs and statemented children, as they, by their very nature, progress at a slower level than other children. Many schools who have 100% SATs results make life very difficult for children with special needs, and so their parents take them elsewhere, to schools such as ours where we try to be inclusive and to educate children for life rather than for tests. Furthermore, this year the rules for extra time, test breaks or readers have been tightened, so it will be even more difficult to get the Level 4s.
I hope this goes to explain why some schools and teachers are so anal, stressed up and obsessive about results. At our school, we try very hard not to be, but it really doesn't do us any good, professionally.