I think the currently accepted answer is incorrect on a number of points. The official California Proposition 65 (aka OEHHA) site FAQ, has more accurate information. There is also another FAQ from the Attorney General, which answers the question as well. The OEHHA site says:
The purpose of Proposition 65 is to notify consumers that they are being exposed to chemicals that are known to cause cancer and/or reproductive toxicity. Consumers can decide on their own if they want to purchase or use the product. A Proposition 65 warning does not necessarily mean a product is in violation of any product-safety standards or requirements. For additional information about the warning, contact the product manufacturer.
The currently accepted answer claims that "Proposition 65 requires warnings if somebody may be exposed to a substance that has a 1 in 100,000 chance", which is not true. Simply being exposed to a chemical that has a certain risk does not make the company required to post a warning. The chemical also has to be on the list. There could be substances which have risk, but are not on the list, and thus they are not required to post a warning.
Here is a quote directly from the OEHHA site, which shows the substance not only has to be on the list, but also has to be in a high enough concentration to create an unsafe exposure:
Proposition 65 applies only to exposures to listed chemicals. It does not ban or restrict the use of any given chemical. The concentration of a chemical in a product is only one part of the process to determine whether consumers must be warned about an exposure to a listed chemical.
The currently accepted answer is also incorrect in that it claims "However, there is nothing preventing warnings even if there is no risk whatsoever." This is blatantly false, because the law allows a business to prove that their use falls below the acceptable use threshold. Here is a quote directly from the California Attorney General's site:
Exposures that pose no significant risk of cancer: A warning about listed chemicals known to cause cancer ("carcinogens") is not required if the business can demonstrate that the exposure occurs at a level that poses "no significant risk." This means the exposure is calculated to result in not more than one excess case of cancer in 100,000 individuals exposed over a 70-year lifetime. The Proposition 65 regulations identify "no significant risk" levels for certain carcinogens. The most recent list of no significant risk levels can be found here: http://www.oehha.ca.gov/prop65/getNSRLs.html.
Thus, businesses have the possibility to show their product is safe, and not post a warning even if it contains a chemical from the list. Small companies of less than 10 employees are exempted having to post a warning.
If a large company thinks it's cheaper for them to place warnings on all of their products, than it would be for them to do testing to see if their product is safe for consumers, that seems a bit of a red flag to me.
I found a particular product I purchased came with a warning, but when I looked on the company website though they acknowledged the warning, they wouldn't let their consumers know which offending chemicals were. This law is about the consumers "right to know". If the business posts a warning, but won't let you know what the chemicals are that are the cause for that warning, it seems a bit of a red flag to me as well. If consumer safety is not an important enough issue for a company to do the testing, it seems safer to me to just avoid those products where possible.
One more useful tidbit of information is that, according to the Attorney General, Proposition 65 has been successful in motivating businesses to eliminate or reduce toxic chemicals in numerous consumer products. This law is not only about helping consumers make informed decisions, it's about motivating companies to be more responsible for the safety of their consumers.