Before we start on the specifics of the experiment itself we need to understand how DNA replication occurs on a molecular level. DNA is made up of four different bases; A, C, G and T. Each base is attached to a deoxyribose sugar and a phosphate group. The sugars and phosphates are covalently bonded to each other in a long line to form the backbone of the linear DNA model. This single stranded DNA is not stable and is vulnerable to damage as the bases that carry genetic information are left exposed. This is avoided by storing DNA as a double stranded molecule in which the bases pair between the backbones like the rungs of a ladder. A always pairs with T and C always pairs with G. This is convenient for DNA replication as it means the DNA strands can be separated and used as a template for the new strand.
There are three possible ways to use the DNA template to replicate DNA; conservative, semi-conservatively or dispersive replication. Meselson and Stahl's experiment sought to establish which one was correct. Conservative replication separates the original strands to use as templates for new strands. The new strands combine to form an entirely new double stranded molecule while the original strands re-join so the original molecule is completely conserved. Semi conservative replication uses the original strands as templates but there is no further separation or re-joining, instead the new molecules are a mixture with one side as the original and the other as new DNA. Dispersive replication is similar to semi-conservative replication but the original and new strand constantly swap so that each individual DNA strand is a mixture of old and new.
To work out which method is used they grew E. coli bacteria in a medium containing N15, a heavier isotope of nitrogen, which is an element incorporated in DNA bases. The bacteria were then removed and placed in a medium containing only N14, so that all new DNA would be lighter than the original DNA. By letting the bacteria divide and replicate their DNA and then extracting and separating out the DNA according to weight they would be able to distinguish between these methods.
After the first division half of the DNA will contain N15 and half N14, but the weights will be distributed differently depending on the method of replication used. When the DNA was extracted and separated it made one band, meaning all the DNA molecules were the same weight. They were therefore able to disregard the conservative replication as this would have made two bands, one entirely of N15 and one of N14. In the other two possible methods the strands contain equal amounts of original and new DNA.
To distinguish between semi-conservative and dispersive replication the bacteria were allowed to divide again and the extracted DNA formed two bands. This confirmed that the method of replication was semi conservative because half of the new DNA would be formed using the N15 strand as a template and half with a N14 strand template, so half of the new DNA molecules would be heavier than the other. In contrast dispersive replication would produce DNA that all had an equal proportion of N15 to N14 all of the DNA would be the same weight. This proved that the method of DNA replication is semi conservative.
If I were answering this question in a tutorial I would use a diagram with different colours to represent the different weight strands to explain this as this makes it a lot clearer and easier to follow. I would also recommend doing this in an exam as a correct diagram shows the examiner that you understand the principles of the experiment, but you would need to accompany this with an explanation of how the results they found support the conclusion they made.