Jednička s hvězdičkou is teacher´s evaluation of a pupil´s performance (elementary schools); literary it means number one with an asterisk. The Czech system of school performance evaluation (elementary and secondary schools)uses a five-point scale where 1 means excellent, 2 very good, 3 good, 4 sufficient and 5 insufficient or failed. Asterisk (which does not appear in official reports) means an outstanding homework, essay or presentation, something even better than excellent.
This expression (1*) can also be used metaphorically as an appreciation. E.g. I'll give you jedničku s hvězdičkou (for something).