You haven't specified if which type of cell you are referring to. There are many types of cells and each cell would have different reactions when immersed in a beaker of distilled water. So let us take for example, the red blood cell. A distilled water is hypotonic compared to the solution contained within the cells' membranes. Therefore, the distilled water will diffuse into the red blood cells and cause them to burst. Hope this answers the question.
