Synthetic Phonics is a method of teaching phonics using just the base elements of the individual phonemes.
So each word is built, or synthesised, using the individual sounds which are all blended. So mainstream phonics teachers common letter groupings, such as the /-at/ in 'fat', 'bat', 'cat', 'rat', 'sat', 'mat' and 'pat', Synthetic Phonics purely focuses on the sound that each phoneme (individual sound) and the letter patterns (graphemes) relating to them. So a word like 'fat' will always be decoded from the three sounds /f/, /a/ and /t/, not /f/ and /-at/.
There are around 45 phonemes in English, 220 graphemes and 450 individual relationships between phonemes and graphemes. So many graphemes can represent multiple phonemes. The tricky element of Synthetic Phonics is how the learner deals with alll that irregularity. Often they will choose to rely on a sight-word memorisation technique instead, because it just seems easier in the early stages.
Opponents to Synthetic Phonics believe that it is a boring teaching method, making it hard to absorb for some children. It is also a very technical approach which requres considerable coaching of the teacher to deliver and does not always fit with the natural inclinations of some primary level teachers. And finally it can be hard for the parents of a child to know how to help in a way that complements what is being taught at school.