Språk is the normal word for language. Mål might be an older word? Anyway, it's mainly used in certain contexts, such as modersmål (mother tongue), bokmål (a form of written Norwegian), and dalamål and names of other dialects. Indeed, my dictionary says 'dialect' for mål, but even for 'dialect' the normal Swedish word these days is 'dialekt'.
Interestingly "mål" also has 3-4 other meanings (goal, target, court case, meal...) and in those meanings it's still a commonly used word :) You will always understand from the context which mål it is.