It was, at least in part, because the Jordanians had cooperated greatly with the Israelis under Hussein around this time.

Jordan had always been hesitant to attack Israel. In fact, during the 1967 War, the Israelis believed that the fire coming from Jordan initially was just meant to show solidarity; not to inspire further conflict. It was only when it didn't stop that the Israelis realized the Jordanians were going to get involved, but even then it appeared to be more reluctant and forced than anything else; the defense pact signed with Egypt on May 30 and the fear of being ostracized likely contributed.

Even ignoring this, Jordan also suffered from struggles with the Palestinians to a large degree. One of the largest takers of Palestinian refugees, it was constantly plagued by fedayeen who operated within its borders and outside its control to attack Israel, and it feared retaliation throughout the leadup to the 1967 war as well. This conflict, as well as the conflict between the Palestinians and Hashemites (because the Jordanians wanted Palestine for themselves, not a separate state) only lent to the internal divisions that may have led Jordan to sit it out. There are even numerous instances of attacks by the Jordanians on the Palestinian refugee camps in retaliation for fedayeen operations, and many arrests as well.

Even so, much of the cause for Jordan's failure to join is attributed to the results of the 1967 War. Morris puts it this way:

Having been badly scorched (and deceived by Egypt) in 1967, Hussein was unwilling to plunge into a second adventure. Moreover, Jordan's relations with Egypt and Syria were badly strained: Cairo had severed diplomatic ties with Amman in March 1972; Damascus had done so in 1971. But the preparations for war required a smoothing of ruffled feathers, so in September 1973 Egypt and Syria initiated a last-minute restoration of relations with Amman.

The deception referred to is likely the deception by Egypt in saying that it was winning after Israel's first strike, which emboldened Hussein to act and attack.

Even so, the Jordanians didn't entirely "sit this one out". They may not have directly engaged in the fighting nearly as much, but they contributed to the cause. When Egypt sent out a request for weaponry, financial support, and staff, the Jordanians sent two armored brigades, with 170 tanks and 100 armored personnel carriers. Saudi Arabia sent a battalion of paratroops and a battalion of rumored personnel carriers and moved several brigades of infantry and a number of tanks to Jordan, though these did not participate in the fighting. Part of the problem was that a date for the war was not told to the contributors, so many of the resources didn't reach in time. The Jordanian forces did participate, but only in token amount, which I'll explain a little later.

Jordan, though, was playing a sort of double game. Because of Jordan's strained relations with the other Arab states, Hussein (who had met secretly with Golda Meir 8 times since she took office in 1969, 4 years prior or so) flew to Israel to meet with her again on September 25, 1973. He remarked that the Syrians had placed their troops in offensive formations, and also implied that Egypt would join, though it's not clear if Meir understood it because of how he phrased it. However, it's not apparent he knew about the date, merely that there would likely be war. He had arranged to have his son meet with the Agricultural Minister in Israel on October 7th (the day after the war began) to discuss exploiting Dead Sea minerals together: a sign of both cooperation and his ignorance of the date of impending attack.

Now, to explain the token contribution, some new facts have come to light. As one historian wrote in this article:

For example, on October 10, 1973, four days after the war started, Jordanian Crown Prince Hassan proposed to U.S. Secretary of State Kissinger that King Hussein would update the Israelis on the deployment of his forces and their exact location - and guarantee that Jordan had no intention of having the Jordanian forces meet the Israeli forces. The king personally informed the U.S. ambassador in Amman that the participation of Jordanian soldiers in the war was just part of the facade presented to other Arab countries.

Another example is found in the article as well, according to the historian:

Kissinger asked the Israeli ambassador in Washington, Simcha Dinitz, to keep Israel from attacking the Jordanian unit, explaining the Jordanians would not participate in the fighting and would only be stationed on the battle front. Dinitz told Kissinger Israel official refuses but that unofficially, the unit will not be attacked.

Essentially the Jordanians had a tacit understanding, largely due to U.S pressure and mutual benefit after the thrashing the Jordanians received in 1967 (and their relatively cool relations with the other Arab states) that they would not participate and would stay as neutral as possible without losing face.

Hopefully that paints the picture for you well!

Sources:

Smith, Charles D. Palestine and the Arab-Israeli Conflict. New York: St. Martin's, 1988. Print.

Oren, Michael B. Six Days of War: June 1967 and the Making of the Modern Middle East. Oxford: Oxford UP, 2002. Print.

Morris, Benny. Righteous Victims: A History of the Zionist-Arab Conflict, 1881-2001. New York: Knopf, 2001. Print.