You throw in your ELISA kit to be analyzed, and your target analyte will be caught by the antibodies, even when you dump the sample solution out. Then, you add a primary ELISA kit this is one that also have preferential binding to your analyte. The only difference is that this ELISA kit has a special region in its tail, and it not affixed to the well. The primary ELISA kit will bind to your analyte.
Now you add a secondary ELISA kit, which loves to bind to that special region of the primary ELISA kit. The thing about this secondary ELISA kit is that it has an enzyme at its tail. This enzyme is specialized in converting one molecule to another (let call them molecule A and molecule B). Finally, you wash the well with a solution of molecule A. If the well has your analyte, it will have that train of primary and secondary antibodes, which means it will have the enzyme. Those wells will be converting molecule A into molecule B except molecule B is fluorescent! This is how we detect the presence of our analyte.
Summary: The analyte we want to detect is stuck onto the bottom of the well. Then we add an enzyme to the well and this ELISA kit only sticks if the analyte is present. Then we throw in some substrate for that enzyme. If the enzyme is present, it will convert the substrate into a fluorescent molecule, which is detected.