The aim of every sacrifice is to create a link.
The idea is that a link is created by a process of interchange, of giving and taking.
The process of taking from the Lord is much easier than giving to Him, so I have to find ways to symbolize and structure the act.
The point is that in a sacrifice, I am giving up something of myself, of my property.
Fasting, for example, is a sacrifice because it has the same effect.
There is a beautiful part of the prayer book which says that because we no longer have any sacrifices in the temple I give my blood and my fat and glands by way of fasting.
This is what I call the denial.
In a certain way, I am always in the middle of a process:
I am living, I am breathing, I am doing, I have something.
The link exists already—the bounty, the power, is being given to me at every moment.
Life is being given to me and I try to do something to make the link mutual.
There is a very important idea that is stated in many different ways: that while receiving creates a link, giving makes a deeper link—psychologically and in many other ways.
In a very broad way, every commandment is a small form of sacrifice because it contains this: at a certain point I don't do exactly what I want.
So what is sacrifice?
In a small way, if I want to tell a joke and I don't tell it, that is a sacrifice:
I don't do exactly what I want. It becomes a sacrifice when it is oriented in this way.
–Rabbi Adin Steinsaltz
From a conversation with Rabbi Adin Steinsaltz in The Strife of the Spirit.