this is basically just a word for an experiment where you’re measuring the “amount” of something, such as the activity of an enzyme or the “binding” of a molecule. Typically, the measurements are taken over time and/or while changing some reaction component in order to determine the inherent properties of the thing (as opposed to properties that are more context-dependent). So, for example, in an “activity assay” you might take an enzyme, give it some substrate (molecule to change) and measure the amount of product formed over time. Or you might test a range of enzyme and/or substrate concentrations. “Assay” is often used in the context of enzymes, but it can be used for things other than enzymes – you can measure things like binding, etc. Basically, you just want to figure out “how much” of some property is present – how much substrate- to-product-making power is there? or how much binding power is there? Of course, you need some sort of read-out to measure – this can be something like a color change or differences in the size of bands you see on an electrophoretic gel (indicating a change in product size).