This article refers to resolution as it is used in the context of the World Assembly. For a more general definition, please see the Wikipedia article on the subject.
Resolutions are World Assembly proposals that have reached quorum and have proceeded to vote before the entire WA. Passed resolutions hold the force of law in all current member states, although resolutions adopted prior to April 2008 (when the WA was known as the United Nations) are no longer in effect. Every time a resolution is voted in, members receive a notice from the Compliance Commission, informing them of new laws to bring them into compliance. Only current members are affected by passage, and though leaving the WA doesn't change the effect, it can be reversed through daily issues (or partially reversed if a repeal passes). Nations that join the WA are assumed to have adopted all passed resolutions, even though there is no in-game effect to that nation.
Since Sept. 2004, passed resolutions have been subject to repeal.  The repeal process is almost identical to the proposal process, in that a repeal requires approvals from six percent of the Regional Delegates to be voted on by the WA at large.
The World Assembly maintains a list of passed resolutions, numbered in the order that they pass, but doesn't track or number failed ones. A list of failed resolutions can be found in NSwiki's WA Timeline. Historical UN resolutions, including most failed ones, are listed under UN Timeline.