Dense Rank -Vs- Rank -Vs- Row_Number

Rank => Rank with Gaps (Eg: 1,2,2,4,5)
Dense Rank => Rank without Gaps (Eg: 1,2,2,3,4)
Row_Number => Ordering of rows; no consideration of equal ranks (Eg: 1,2,3,4,5)

Rank over (ORDER BY clause)
Dense_rank over (ORDER BY clause)
Row_number over (ORDER BY clause)

ORDER BY clause can also be replaced by "PARTITION BY x ORDER BY y"

For details see the example here