Mesh Particle Emitters are generally used when you need high control over where to emit particles.
For example, when you want to create a flaming sword:
You should now see particles emitting from the mesh.
Play around with the values in the Mesh Particle Emitter.
Especially enable Interpolate Triangles in the Mesh Particle Emitter Inspector and set Min Normal Velocity and Max Normal Velocity to 1.
To customize the look of the particles that are emitted:
You should now see textured particles emitting from the mesh.