You can see them for yourself here. You will note that the top rankings are overwhelmingly dominated by American universities.
Leiden university ranks other universities in the following way:
The Leiden Ranking 2011/2012 is based on publications in Thomson Reuters’ Web of Science database in the period 2005-2009. Only publications in the sciences and the social sciences are included. Publications in the arts and humanities are excluded because in these domains the bibliometric indicators of the Leiden Ranking do not have sufficient accuracy. Furthermore, only publications of the Web of Science document types article, letter, and review are considered in the Leiden Ranking.
The Leiden Ranking offers the following indicators of the scientific impact of a university:
Mean citation score (MCS). The average number of citations of the publications of a university.
Mean normalized citation score (MNCS). The average number of citations of the publications of a university, normalized for field differences, publication year, and document type. An MNCS value of two for instance means that the publications of a university have been cited twice above world average.
Proportion top 10% publications (PPtop 10%). The proportion of the publications of a university that, compared with other similar publications, belong to the top 10% most frequently cited.
Publications are considered similar if they were published in the same field and the same publication year and if they have the same document type.
Citations are counted until the end of 2010 in the above indicators. Author self citations are excluded. The PPtop 10% indicator is more stable than the MNCS indicator, and we therefore regard the PPtop 10% indicator as the most important impact indicator of the Leiden Ranking.
In other words it looks at how often papers coming out of a given university are cited in other papers.
That rather explains the American dominance. There are a LOT of American universities (around 7,000 on some counts -- depending on what you define as a university). So what we are seeing is that all those American researchers mostly cite papers by other Americans. There are many reasons why that might be so with the excellence of the cited paper being only one of the reasons.
Being personally acquainted (via conferences etc.) with other people working in your field is another obvious reason. I know from my own experience during my research career that the heaviest use of my papers mostly came from people I knew personally from conferences.
So although the Leiden rankings are the most objective of the rankings available they are really only useful in ranking American universities. As rankings of universities worldwide they are essentially useless.
It is therefore all the more to the credit of the occasional non-American university that crept into the list. The highest ranking Australian university was the ANU, ranked 114th. The ANU was of course designed from the beginning as a research-heavy university so that is not unexpected.
The University of Melbourne came 163rd ,the University of Queensland (my alma mater) was 170th but the University of Sydney was 290th.
Most other rankings of world universities place Australian universities much higher.