Assays during drug discovery
An assay may be thought of as a trial or test that is designed to quantitatively determine the amount of a substance in a sample.  

Thus a biochemist might use a protein assay to quantitatively determine the amount of protein in a sample, or a pharmacologist might assay a sample to quantitatively determine the amount of drug present, or an enzymologist might carry out an enzyme assay to determine the amount of enzyme activity in a sample.

Let's take the case of the enzymologist. I take a liver sample, homogenize it, centrifuge and take the supernatant (soluble) fraction. I want to quantitatively determine the amount of a given enzyme activity. 

I do this by performing a test by (say) adding a sample of the supernatant to a cocktail that 'does something' only if the enzyme of interest is present.  The 'do something' could be a color change, where the cocktail  contains  everything needed for the enzyme to work (all substrates, cofactors etc) and where the enzyme transforms one of the substrates to a coloured product.  I now have an enzyme assay which tells me if the enzyme is present (the trial), which may be made quantitative with reference to the amount of color produced in a given time.

As I remember things, Sherlock Homes was pretty good at the assays, using them to make trials of his geological samples, but I cannot find the quote.