Pursuant is used mainly in a legal sense to say something's in accordance with a particular law, ruling, or request. It's followed by the word "to." So you might say, "Pursuant to the judge's request, we'll provide additional testimony."
Pursuant sounds a bit like pursue, and has a related meaning in the sense of "following" — but in this case it's an agreement or ruling that you're following. Pursuant comes from the French word pursuer, meaning "to follow with hostile intent." Over time the word lost its sense of hostility — unless of course you're angry when the lawyer tells you that pursuant to the investment policy, you can't withdraw all your money and run away to Paris.