Syntactic analysis is an activity where people take a sentence in a language and analyse its grammatical components. It can be very simple (for example, pointing out the subject and verb of a sentence) or more complex. A complete syntactic analysis can be really complex.
I did a lot of syntactic analysis during secondary school. I was doing my German homework and seeing a lot of very long, very complex sentences and wondered if people in Europe also do syntactic analysis at school.