A three dimensional model (3D model) is a model of an object or event that takes into account variations on all three dimensions, contrasting it with a one or two dimensional model. An analytical model might be 3D but very likely something termed a 3D model is a computerized model.
A 1D model is often used for spherical or round objects, and at each distance from the center of the object (a spherical shell shaped volume), treats processes as occurring identically around the sphere. A 3D model accommodates a situation where on different portions such a shell, different things are happening. An example might be convection, in which in portions of some shell, a fluid is rising, i.e., moving away from the center, and in other parts, fluid is falling. A 1D model can handle such convection only by "averaging" the effects of convection around the entire shell, which skips detail.
The 1D model solved numerically has an advantage of requiring less calculation: a calculation must be done for each of a selected number of distances from the center, but it does not do separate calculations for different regions equidistant from the center. Thus the computing required to run the model can be much less: in some cases, in the time it takes to run a single experiment with a 3D model once, thousands or millions of experiments could be run on a 1D model, and the difference can be weeks versus seconds for a single run. Thus there is a trade-off regarding whether the 1D model offers sufficient accuracy, information and resource-savings to be of use. Due to this potentially large resource advantage, drastic simplifications are often tolerated in a model in order to avoid 3D modeling (the term spherical cow makes fun of this notion). Year by year, faster computers are developed and models are improved, and more phenomena are modeled in 3D. As of 2017, it is reported that 3D modeling of core collapse supernovae is just becoming practical.
Another advantage of the 1D model is that it is more likely to be solved analytically, i.e., equations are available to determine the values at any distance from the center without using results of calculations of conditions at other distances. This results in even more efficiency and flexibility, and makes them more useful for incorporation within in models of encompassing phenomena. For example, to model an entire cluster of stars, a model of a single star might be a piece of it, and the more efficient that sub-model, the larger a cluster can be modeled.
An advantage of a 3D model is that it can handle potentially non-spherical phenomena, e.g., molecular clouds. 1D models offer information about a non-spherical phenomenon only according to its similarity to the same phenomenon when it happens to be spherical. In some cases, this is a useful approximation.
This model distinction (1D, 2D, 3D) applies to models of stars, e.g., their structure and evolution, for planetary atmospheres, e.g., their structure, weather, and climate, for planet statics, for supernovae, for clouds such as molecular clouds, HII region, HI region, for galaxies, and galaxy clusters.
2D models are also used, typically choosing appropriate poles on the sphere, and independently modeling activities at multiple distances around a circumference from a pole as well as multiple distances from the center of the sphere. They model any activity as the same if it is the same distance from the center as well as the same distance from the poles. Their computational cost is between 1D and 3D models, giving another choice in the value/cost tradeoff. They can be useful when rotation is the main complication to 1D modeling, producing a circular symmetry, e.g., disks, tori, polar jets, and in such simulations can be very advantageous. Another useful case is when external energy, e.g., incoming electromagnetic radiation, is entering (largely) from a single direction, such as a planet tidally locked to its host star. The shapes of objects as modeled tend to have circular symmetry, which can result in a pottery-like shape. To what degree this hurts the model's accuracy depends upon the phenomena.