glLightModel sets the lighting model parameter. 
pname names a parameter and params gives the new value.  There are three
lighting model parameters:

GL_LIGHT_MODEL_AMBIENT

params contains four
integer or floating-point values that specify the ambient RGBA intensity
of the entire scene.  Integer values are mapped linearly such that the most
positive representable value maps to 1.0, and the most negative representable
value maps to -1.0.  Floating-point values are mapped directly.  Neither integer
nor floating-point values are clamped.  The initial ambient scene intensity
is (0.2, 0.2, 0.2, 1.0). 

GL_LIGHT_MODEL_COLOR_CONTROL

params must be either
GL_SEPARATE_SPECULAR_COLOR or GL_SINGLE_COLOR.  GL_SINGLE_COLOR specifies
that a single color is generated from the lighting computation for a vertex. 
GL_SEPARATE_SPECULAR_COLOR specifies that the specular color computation
of lighting be stored separately from the remainder of the lighting computation. 
The specular color is summed into the generated fragment's color after
the application of texture mapping (if enabled).  The initial value is GL_SINGLE_COLOR. 

GL_LIGHT_MODEL_LOCAL_VIEWER

params is a single integer or floating-point
value that specifies how specular reflection angles are computed.  If params
is 0 (or 0.0), specular reflection angles take the view direction to be
parallel to and in the direction of the -z axis, regardless of the location
of the vertex in eye coordinates.  Otherwise, specular reflections are computed
from the origin of the eye coordinate system.  The initial value is 0. 

GL_LIGHT_MODEL_TWO_SIDE

params is a single integer or floating-point value that specifies whether
one- or two-sided lighting calculations are done for polygons.  It has no effect
on the lighting calculations for points, lines, or bitmaps.  If params is
0 (or 0.0), one-sided lighting is specified, and only the front material
parameters are used in the lighting equation.  Otherwise, two-sided lighting
is specified.  In this case, vertices of back-facing polygons are lighted
using the back material parameters, and have their normals reversed before
the lighting equation is evaluated.  Vertices of front-facing polygons are
always lighted using the front material parameters, with no change to their
normals.  The initial value is 0. 

In RGBA mode, the lighted color of a vertex
is the sum of the material emission intensity, the product of the material
ambient reflectance and the lighting model full-scene ambient intensity,
and the contribution of each enabled light source.  Each light source contributes
the sum of three terms: ambient, diffuse, and specular.  The ambient light
source contribution is the product of the material ambient reflectance
and the light's ambient intensity.  The diffuse light source contribution
is the product of the material diffuse reflectance, the light's diffuse
intensity, and the dot product of the vertex's normal with the normalized
vector from the vertex to the light source.  The specular light source contribution
is the product of the material specular reflectance, the light's specular
intensity, and the dot product of the normalized vertex-to-eye and vertex-to-light
vectors, raised to the power of the shininess of the material.  All three
light source contributions are attenuated equally based on the distance
from the vertex to the light source and on light source direction, spread
exponent, and spread cutoff angle.  All dot products are replaced with 0
if they evaluate to a negative value. 

The alpha component of the resulting
lighted color is set to the alpha value of the material diffuse reflectance. 

In color index mode, the value of the lighted index of a vertex ranges
from the ambient to the specular values passed to glMaterial using GL_COLOR_INDEXES. 
Diffuse and specular coefficients, computed with a (.30, .59, .11) weighting
of the lights' colors, the shininess of the material, and the same reflection
and attenuation equations as in the RGBA case, determine how much above
ambient the resulting index is.