SATs are national tests that children currently sit twice during their time at primary school - once after the end of Key Stage 1 (Year 2) and again at the end of Key Stage 2 (Year 6). They're actually called End of Key Stage Tests and Assessments, but the acronym SATs (from another, earlier set of tests) has stuck.
The Key Stage 1 tests are all teacher-assessed (no external marking but some external moderating) and are meant to be low-key, hardly-know-you're-doing-it kind of affairs. Tests are being administered in arithmetic and in English reading. There is another, optional test of English grammar, punctuation, and spelling. There will also be a teacher assessment of your child's standard in science, although there is no formal science test.
Teacher assessments will be based on each pupil's scaled score (for more about scaled scores, see Key Stage 2 marking, explained, below). Teachers will convert each child's number of marks earned into an equivalent "scaled score", and will use that to determine whether each child has met, exceeded, or fallen short of the national standard.
The Key Stage 2 tests are a bit more formal: done on a set day and (mainly) marked externally. There are papers in English reading comprehension, grammar, punctuation, and spelling, and in maths (including arithmetic and mathematical reasoning).
This year (2016) there are additional questions designed to assess new areas of core subjects in the national curriculum, to reflect curriculum changes that have been made and to enable your child to be fully assessed on what they have been taught. It's already been noted that these tests are significantly more difficult than SATs from previous years, with even able children struggling to understand the nature of the questions - so if your child has been frustrated by them this year, you're not alone.
You will receive separate teacher judgement assessments - besides the formal test results - in English reading and mathematics, and a teacher judgement assessment in science. There will be no formal Key Stage 2 test for science.
Your child will be marked in three ways. Firstly, they will receive a raw score corresponding to the number of marks they achieved. Secondly, this score will be weighted to produce a "scaled score", for which the "expected result" benchmark will be 100. Thirdly, you'll receive a confirmation of whether or not your child achieved the expected standard.
Previously, SATs were marked using "levels" - evaluations of whether your child was working at, above, or below the expected standard for their age. These were represented as numbers: an eleven-year-old's expected standard, for instance, was a level 4. Levels have now been abolished, in response to concerns about their reliability. From 2016 onwards, national SATs outcomes will be reported only in the form of scaled scores.