What does a strong negative correlation mean?

A weak positive correlation would indicate that while both variables tend to go up in response to one another, the relationship is not very strong. A strong negative correlation, on the other hand, would indicate a strong connection between the two variables, but that one goes up whenever the other one goes down.

Is a negative correlation still strong?

The strength of a correlation relationship is quantified by its correlation coefficient, the strongest possible being "perfectly" correlated. ... In general, -1.0 to -0.70 suggests a strong negative correlation, -0.50 a moderate negative relationship, and -0.30 a weak correlation.