Occam's Razor is the principle that the simplest explanation for phenomena should be adopted wherever possible.
The immediate difficulty in applying Occam's Razor is the question of how we define "simplicity". A broadly-accepted interpretation is to interpret the principle as meaning that the simplest explanation is one that has the minimum numbe rof entities - an additional sophisticatio nbeing that mimimisong the number of objects is of secondary importance to minimising the number fo types of object.
So, for instance, in the case of Darwinian Evolution, Charles Darwin's theory proposed that rather than the world containign millioms of distinct and individually created species, the distict traits of different groups of plants and animals could be intepreted as manifestations of a single overall body of livign creatures, whose different diverging populations eventually became reproductively incompatible, producing the effect of speciation.
Objects and object types
In early astronomy it might have seemed reasonable to categorise the range of astronomical bodies into four groups, the Earth, Moon, Sun and stars. Stars could be divided into fixed stars and wandering stars (planets). With the invention of the telescope, the realisation that the planets were also spherical bodies, and that Jupiter also had moons meant that Occam's Razor favoured an interpretation in which Earth was simply another planet, all the planet rotated around the Sun (or ratehr around a common centre of gravity shared with the Sun), and that other stars were simply other suns and might have planets and perhaps life of their own (Bruno).
Although this new world-view increased the number of objects in the universe, it reduced the number of distinctly different objects. In terms of computer programming, we can say that the revised theory increased the number of class members, but reduced the total number of classes.
Local bias and scale-sensitivity
One of the difficulties of Occam's Razor is that it can cut in different directions depending on the range of phenomena that we know about or choose to include. Sometimes the simplest solution based on limited data is no longer the simplest once additional effects and information is incorporated into a model. This can lead to pathological decision-making if we forget that Occam's Razor applied to artificially small sets of data can produce conclusions that do not survive larger data-sets.
Relativity theory applies Occam's Razor to argue against the assumption that the universe distinguishes between "moving" and "stationary" bodies. For the case of simple constant-velocity rectilinear motion, the argument that we cannot tell who is really moving or not leads to Galileo and Newton's system. Mach's Principle then argues that the same reductionism should also be applied to rotation and acceleration – rather than assuming an arbitrary absolute reference for these motions and their associated forces, we can assume that the physics of all motion is purely relative ('General Principle of Relativity, Democratic principle), as long as we are allowed to make make the laws of gravitation more complex.
Special and general relativity
As an example of local bias, we can look at Einstein's special and general theories of relativity. If we ignore gravitational effects, and accelerational and rotational effects, and the effects of particulate matter on light, then special relativity's flat-spacetime model clearly explains the remaining phenomenology more concisely than a more complex theory based on curvature principles - "flat" is simpler than "curved".
However, once we admit that these excluded effects are real and involve curvature of the light-grid, we need to reexamine whether special relativity really is fundamental physics. If we look at mid-Twentieth Century relativity theory, with its two separate sets of physical laws for curved and flat spacetime, and its incompatibility with quantum theory, and compare this with a hypothetical Cliffordian universe in which curvature is fundamental, there is no special theory underlying GR, and GR appears dual with quantum descriptions, then Occam's Razor seems to shift in favour of the unified model, even if it does not seem to include such simple entry-level foundations.