An earmark is a legislative provision which Congress uses to direct funds to be spent on specific named projects and passed without examination: particularly, projects in the home districts of sponsoring members (see pork barrel). Earmarking allows Federal agencies to bypass regulatory determinations. Some earmarks are criticized for the perceived frivolous nature of the project. Earmarking is part of the process of awarding "pork barrel" projects.
"OMB defines earmarks as funds provided by the Congress for projects or programs where the congressional direction (in bill or report language) circumvents Executive Branch merit-based or competitive allocation processes, or specifies the location or recipient, or otherwise curtails the ability of the Executive Branch to manage critical aspects of the funds allocation process." 
The term "earmark" comes from cattle and hog slaughtering houses. When cattle are being loaded for slaughter, a particular animal may be singled out for a special purpose, such as breeding; the animal would receive an earmark, so those loading the cattle would see the earmark, and direct the particular animal for its individual purpose. In much the same way, as money is being appropriated for operations of the federal government, or as "appropriations are being loaded", an earmark designates funds to be spent in a specific Congressional members state or district. The process has become highly specialized over time, even designating specific businesses to award no-bid contracts to, or specific plots of land to be purchased from specific owners of land to build a federal project.
The process of earmarking has become potentially abusive in circumventing existing laws and awarding no-bid contracts. By example, let's say Donor A owns a plot of land and makes a contribution to a member of Congress, and Builder B happens to be the members brother-in-law. And the member has earned a pork barrel project from the Congressional leadership for his cooperation on other measures. A Congressional Appropriation for, let's say, a new Post Office to be built in his district is designated or earmarked. Into the appropriation law can be written earmark instructions to purchase the land from Donor A and award the construction contract earmarked to Builder B, thus by law, by-passing open bidding requirements.