In the "Roadrunner" cartoons, the coyote is out to get the roadrunner. (A coyote is like a small wolf, a roadrunner is a small bird that can run quickly). The coyote is hunting or stalking the roadrunner. The coyote wants to catch the roadrunner, kill it, and eat it. Figuratively, among people, it means that person A is stalking or hunting person B and wants to do person B harm. Teacher: "I have my eye on you! If I catch you texting on your cell phone again, I'm confiscating the phone and giving you detention!" Student to friend: "It's unfair! The teacher is out to get me!"

It means to harm someone. The harm could take many forms: career-wise, emotionally or physically. Example: the democrats are out to get Trump for his policies.

To be out to get someone means to INTEND to harm someone - not (usually) by planning a physical attack, but usually by planning to damage someone's prosperity, happiness or reputation. The important thing to note is that the expression 'to be out to get someone' is always about the intention to cause harm, not the actual act.