Most of the country's most prestigious colleges and universities have low student / faculty ratios. However, they are also schools where a high research and publication expectation is placed on the faculty. As a result, the faculty tend to teach fewer courses than at schools where research is valued less and teaching is valued more. You are likely to find that a prestigious college like Williams with a 7 to 1 student / faculty ratio has class sizes that aren't much different from a place like Siena College with a 14 to 1 ratio.
At a well-regarded research university, many of the faculty members spend considerable time not just on their own research, but also supervising graduate research. This gives them less time to devote to undergraduates than the faculty at an institution with primarily undergraduate enrollment.
While you should interpret the student / faculty ratio carefully, the ratio still says a lot about a school. The lower the ratio, the more likely it is that your professors will be able to give you personal attention. When you find a ratio over 20 / 1, you'll often discover that classes are big, the faculty are overworked, and your opportunities for one-on-one interaction with your professors are greatly diminished. I consider a healthy ratio to be 15 to 1 or lower, although some universities deliver excellent instruction with a higher ratio.
Note that the ratio is typically calculated using full-time faculty or their equivalent (so in many calculations, three 1/3-time employees would count as a single full-time faculty member). Different schools will calculate the number somewhat differently. For example, does the university count graduate student instructors? Does the school count faculty who spend all their time on research rather than undergraduate teaching? In other words, the student / faculty ratio is not a precise or consistent science.
A related and more meaningful piece of data is the average class size. This is not a number that all colleges report, but you should feel free to ask about class size when visiting campus or talking with an admissions officer. Does the college have large freshman lecture classes? How big are upper-level seminars? How many students are in a lab? You can often learn a lot about class size by looking at the course catalog. What are the maximum enrollments in different types of classes?