Yeah, once an effect goes on the stack, that effect will happen. Usually in response, you will try to protect the target of the effect or change the effect. It gets really confusing when you have to pay attention to where a sacrifice is on a card.
For example (I might mess this up), if a card say Tap, Sacrifice ____ : Gain 10 billion life. As soon as you tap and sacrifice, I can't really stop it with anything but a card that stops activated abilities. You have activated that, it goes on the stack.
Now, if it says Tap: Sacrifice ______ , then gain 10 billion life. I can remove that card from the game in response, and you won't gain the life.
Where priority really comes in is during the phases. If it is your turn, you will have priority first during every phase, then pass priority to your opponent, will probably do nothing, then you move on. An example of this mattering is something like:
Your Main Phase one, you tap mana then bring out Jace. Your opponent doesn't respond, priority is now your again, so you can use his ability if you want and your opponent can't stop you. But say you don't, so it goes to and you have nothing else to do in Main Phase one, you have now passed priority to your opponent. During this time your opponent chooses to use Hero's Downfall on Jace, you can respond, but only at instant speed, meaning you can't use the ability now and put it on the stack, Since Planeswalker abilities are sorcery speed.
Like I said, probably messed something up, but it is one of the nuances of the game that can lead to big swings in Eternal formats, where there are cards for every situation. The best tool to get better at understanding this, besides playing with Pros, or with a judge watching the whole match, is to play MTGO. Really forces you to stick to the rules and learn all of that.
