To draw a GameObject on the screen, the engine has to issue a draw call to the graphics API (such as OpenGL or Direct3D). Draw calls are often resource-intensive, with the graphics API doing significant work for every draw call, causing performance overhead on the CPU side. This is mostly caused by the state changes done between the draw calls (such as switching to a different Material), which causes resource-intensive validation and translation steps in the graphics driver.
Unity uses two techniques to address this:
Built-in batching has several benefits compared to manually merging GameObjects together; most notably, GameObjects can still be culled individually. However, it also has some downsides; static batching incurs memory and storage overhead, and dynamic batching incurs some CPU overhead.
Only GameObjects sharing the same Material can be batched together. Therefore, if you want to achieve good batching, you should aim to share Materials among as many different GameObjects as possible.
If you have two identical Materials which differ only in Texture, you can combine those Textures into a single big Texture. This process is often called Texture atlasing (see the Wikipedia page on Texture atlases for more information). Once Textures are in the same atlas, you can use a single Material instead.
If you need to access shared Material properties from the scripts, then it is important to note that modifying Renderer.material creates a copy of the Material. Instead, use Renderer.sharedMaterial to keep Materials shared.
Shadow casters can often be batched together while rendering, even if their Materials are different. Shadow casters in Unity can use dynamic batching even with different Materials, as long as the values in the Materials needed by the shadow pass are the same. For example, many crates could use Materials with different Textures on them, but for the shadow caster rendering the textures are not relevant, so in this case they can be batched together.
Unity can automatically batch moving GameObjects into the same draw call if they share the same Material and fulfill other criteria. Dynamic batching is done automatically and does not require any additional effort on your side.
Because it works by transforming all GameObject vertices into world space on the CPU, it is only an advantage if that work is smaller than doing a draw call. The resource requirements of a draw call depends on many factors, primarily the graphics API used. For example, on consoles or modern APIs like Apple Metal, the draw call overhead is generally much lower, and often dynamic batching cannot be an advantage at all.
Static batching allows the engine to reduce draw calls for geometry of any size provided it shares the same material, and does not move. It is often more efficient than dynamic batching (it does not transform vertices on the CPU), but it uses more memory.
In order to take advantage of static batching, you need to explicitly specify that certain GameObjects are static and do not move, rotate or scale in the game. To do so, mark GameObjects as static using the Static checkbox in the Inspector:
Using static batching requires additional memory for storing the combined geometry. If several GameObjects shared the same geometry before static batching, then a copy of geometry is created for each GameObject, either in the Editor or at runtime. This might not always be a good idea; sometimes you have to sacrifice rendering performance by avoiding static batching for some GameObjects to keep a smaller memory footprint. For example, marking trees as static in a dense forest level can have serious memory impact.
Internally, static batching works by transforming the static GameObjects into world space and building a big vertex and index buffer for them. Then, for visible GameObjects in the same batch, a series of simple draw calls are done, with almost no state changes in between. Technically it does not save 3D API draw calls, but it saves on state changes between them (which is the resource-intensive part). Batches are limited to 64k vertices and 64k indices on most platforms (48k indices on OpenGLES, 32k indices on macOS).
Currently, only Mesh Renderers, Trail Renderers, Line Renderers, Particle Systems and Sprite Renderers are batched. This means that skinned Meshes, Cloth, and other types of rendering components are not batched.
Renderers only ever batch with other Renderers of the same type.
Semi-transparent Shaders usually require GameObjects to be rendered in back-to-front order for transparency to work. Unity first orders GameObjects in this order, and then tries to batch them, but because the order must be strictly satisfied, this often means less batching can be achieved than with opaque GameObjects.
Manually combining GameObjects that are close to each other can be a very good alternative to draw call batching. For example, a static cupboard with lots of drawers often makes sense to just combine into a single Mesh, either in a 3D modeling application or using Mesh.CombineMeshes.