1. to address, to bring up (For issues or topics. They're the direct object then.)
2. to approach, to start talking to someone (usually a stranger) ("jemanden ansprechen" - usually because you want or need something, like help or a date.)
3. to appeal to, to be attractive to ("jemanden ansprechen" - this is mostly used for things that are appealing. Like the color of the curtains for instance. It sounds fairly unemotional.)
4. to respond to ("ansprechen auf-Acc" - ONLY in a sense of systems or sensors reacting to some sort of excitement or input.)