An oath, according to the American Heritage Dictionary, is "a solemn, formal declaration or promise to fulfill a pledge, often calling upon God or a god as witness."
We normally associate oaths with courtrooms. A witness takes the stand, raises their right hand, and swears to tell the truth, the whole truth, ... etc.
Or when an oath of office is administered to a public official -- for example, the recent inauguration of President Obama.
Although not all presidents have taken the oath of office in front of the U.S. Capitol in Washington. Lyndon Johnson was sworn in as President of the United States aboard Air Force One.
An oath can be administered for a variety of reasons, and in almost any location.
So what does all this have to do with Colorado mobile notaries?
It is possible for someone in Colorado to give a testimony for a legal proceeding -- over the telephone -- to people in another state. The person making the statements can do it from their home. However, in order for this person to be put under oath, it has to be done in the presence of someone in Colorado who has the power to administer oaths.
Colorado law gives notaries the power to administer oaths. [CRS 12-55-110(b)]

So a Colorado mobile notary is called to go to the person's home to administer the oath. It is done in such a way that the people on the other end of the phone can hear the person taking the oath. ('Do you ______ solemnly swear ...?')
They are then satisfied that the statements that the person is going to make over the phone will be made while that person is under oath. There could be severe penalties if the person makes a false statement. The mobile notary doesn't have to be present while the person is being questioned -- only for administering the oath.
That is the role that I played this morning. I was called to swear someone in so that they could give their testimony over the phone. First I asked to see the person's identification so that I could properly identify him. I recorded the notary act in my journal. After that, he made the phone call. I was asked to identify myself and give my commission expiration date. I then asked the person to raise his right hand and I swore him in. Once he was sworn in, I left. I had done all that I needed to do.
If a person in Colorado can't personally appear before a judge in another state, a mobile notary can be used. A mobile notary can be a vital link, and provide this kind of service to clients all across the country who need to take statements from someone while under oath.
I used to be a notary out here until the lawyers in this state affirmed that oaths could cost me notable amounts of cash. They wanted to stop the refi closing notaries were doing. Now you need to be on a lawyer's staff. I let the banks do the rest of the stuff.