Density and Mesh Scale:
Particles are randomly spread across a mesh surface with the Scatter node. Density is a value that means how many particles per m² (or cm² or any unit you are using in Maya) is going to be placed in the mesh. Therefore, it is dependent of the mesh size:
Scaling down a mesh will require to increase the density to keep the same look of the original hair. Additionally, length and width parameters need to be lowered, since they are also scale dependent. It is really important to not scale the mesh in animation or render scenes without adjusting this parameters as well.
In my workflow, I usually keep the Density field at 1 and change the Density Multiplier only. Textures or groom mapping is going to override the Density field when plugged, so the value you put there is not going to be used in this case, only the Multiplier.
At the Yeti's node, you can control the density that will appear only the render. This number will multiply the amount set in the all the scatter nodes in render time. It is very useful to improve the performance of the viewport and the manipulation of the graph, since it will only calculate an small amount of fibers.
The final equation that stipulates the amount of particles in the mesh is:
Density x Density Multiplier x Render Density
Render View: Render Density = 1, no changes compared to the viewport
Render View: Render Density = 10, number of particles increased
The same idea is applied to Render Width and Render Length
Lock density is an option that disables the Render Density multiplication of this scatter node. It means that the same amount of particles visible in the viewport will appear in the final render, regardless of the value set in Render Density.
I usually use this option when instancing objects or feathers, where I want an exactly number of particles. Other case is when creating clumping guides. This way I guarantee the same clumping distribution even if the overall fur density is decreased to improve render time.