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The data here is from a core sample, drilled into the sediment on a sunken atoll in the Marshall Islands.
The numbers down the left hand side indicate the depth (in Meters Below Sea Floor) at which each group of fossils was found. As is usual in geology, the diagram gives the data for the deepest (oldest) fossils at the bottom, and the upper (youngest) fossils at the top. This core cannot be used below 100 MBSF because that sediment has been heavily disturbed ("reworked"). However, things are smooth above that, except for the two unconformities shown by horizontal wavy lines. An unconformity just means that there was some sort of gap or break. However, the deposition was continuous and uncomplicated above and below the unconformities. (Those unconformities are local to this drill site, and do not appear in the fossil sequences found elsewhere.)
The numbers down the right side give the age, as determined from reversals of the Earth's magnetic field. The age is given in "Ma", that is, in Millions of years Ago.
The dark vertical lines indicate the timespan for four different kinds of fossils. Click for pictures and descriptions of the fossils. The important point to notice here is that variation arose over a long period of time, and one of the variants went forward as a separate species.
Even if the scientific time scale troubles you, you can see that there is a pattern of biological change spread through a considerable depth of sediment.