In analytical and organic chemistry, elution is the process of extracting one material from another by washing with a solvent: washing of loaded ion-exchange resins to remove captured ions, or eluting proteins or other biopolymers from a gel electrophoresis or chromatography column.
In a liquid chromatography experiment, for example, an analyte is generally adsorbed by ("bound to") an adsorbent in a liquid chromatography column. The adsorbent, a solid phase, called a "stationary phase", is a powder which is coated onto a solid support. Based on an adsorbent's composition, it can have varying affinities to "hold onto" other molecules—forming a thin film on the surface of its particles. Elution then is the process of removing analytes from the adsorbent by running a solvent, called an "eluent", past the adsorbent-analyte complex. As the solvent molecules "elute", or travel down through the chromatography column, they can either pass by the adsorbent-analyte complex or displace the analyte by binding to the adsorbent in its place. After the solvent molecules displace the analyte, the analyte can be carried out of the column for analysis. This is why as the mobile phase, called an "eluate", passes out of the column, it typically flows into a detector or is collected by a fraction collector for compositional analysis. 
Predicting and controlling the order of elution is a key aspect of column chromatographic and column electrophoretic methods.