I have yet to find a source that lays this out explicitly, but from the examples I could find, it is not too hard to infer the meaning of these sections.
To start with (and possibly point you in the right direction to look for more information), this type of *.wfn file was developed as the input format for AIMPAC and quickly spread to be used as an output format for a number of electronic structure programs (e.g. Gaussian, Q-Chem, GAMESS) and an input format for wavefunction analysis (e.g. Multiwfn). So this format isn't particular to Gaussian.
To give another/smaller example to work from, I'll pull sections from a wavefunction file I found with a fork of AIMPAC
Section 1
Formate anion 6-31++G**
GAUSSIAN 12 MOL ORBITALS 104 PRIMITIVES 4 NUCLEI
C 1 (CENTRE 1) 0.00000000 0.00000000 0.57942804 CHARGE = 6.0
O 2 (CENTRE 2) 0.00000000 2.11695431 -0.38686460 CHARGE = 8.0
O 3 (CENTRE 3) 0.00000000 -2.11695431 -0.38686460 CHARGE = 8.0
H 4 (CENTRE 4) 0.00000000 0.00000000 2.71326541 CHARGE = 1.0
The first line is a title card and just below that I believe it records that the orbitals discussed below are Gaussian type, not that the data was produced by Gaussian.
The rest of the line tells you the number of molecular orbitals, the number of primitive Gaussian basis function, and the number of nuclei in your molecule. The follow lines give the element symbol, a number label for each center, their (presumably) Cartesian coordinates, and the charge of the nuclei.
Section 2
CENTRE ASSIGNMENTS 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
CENTRE ASSIGNMENTS 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2
CENTRE ASSIGNMENTS 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
CENTRE ASSIGNMENTS 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
CENTRE ASSIGNMENTS 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4
CENTRE ASSIGNMENTS 4 4 4 4
The previous section mentioned the number of primitives (104). This section tells you which center each of these primitives belongs to. For example, the eight "4" at the end tell you there are 8 primitives associated with the 4th center (H).
Section 3
TYPE ASSIGNMENTS 1 1 1 1 1 1 1 1 1 2 2 2 3 3 3 4 4 4 1 2
TYPE ASSIGNMENTS 3 4 1 2 3 4 5 6 7 8 9 10 1 1 1 1 1 1 1 1
TYPE ASSIGNMENTS 1 2 2 2 3 3 3 4 4 4 1 2 3 4 1 2 3 4 5 6
TYPE ASSIGNMENTS 7 8 9 10 1 1 1 1 1 1 1 1 1 2 2 2 3 3 3 4
TYPE ASSIGNMENTS 4 4 1 2 3 4 1 2 3 4 5 6 7 8 9 10 1 1 1 1
TYPE ASSIGNMENTS 1 2 3 4
Now that we know to which centers the primitives belong, we need to know what type of Gaussian these are (e.g. $\mathrm{s, p_x, p_y, p_z, d_{xx}, d_{xy}}$, etc). I don't know the exact correspondence, but it seems to be
- $\mathrm{s}=1$
- $\mathrm{p}=2-4$
- $\mathrm{d}=5-10$
In the *.wfx format (based on *.wfn, see below), I can confirm that
1=S, 2=PX, 3=PY, 4=PZ, 5=DXX, 6=DYY, 7=DZZ, 8=DXY, 9=DXZ, 10=DYZ, where the format seems to assume Cartesian rather than spherical Gaussians.
Section 4
EXPONENTS 0.3047525E+04 0.4573695E+03 0.1039487E+03 0.2921016E+02 0.9286663E+01
EXPONENTS 0.3163927E+01 0.7868272E+01 0.1881289E+01 0.5442493E+00 0.7868272E+01
EXPONENTS 0.1881289E+01 0.5442493E+00 0.7868272E+01 0.1881289E+01 0.5442493E+00
EXPONENTS 0.7868272E+01 0.1881289E+01 0.5442493E+00 0.1687145E+00 0.1687145E+00
EXPONENTS 0.1687145E+00 0.1687145E+00 0.4380000E-01 0.4380000E-01 0.4380000E-01
EXPONENTS 0.4380000E-01 0.8000000E+00 0.8000000E+00 0.8000000E+00 0.8000000E+00
EXPONENTS 0.8000000E+00 0.8000000E+00 0.5484672E+04 0.8252349E+03 0.1880470E+03
EXPONENTS 0.5296450E+02 0.1689757E+02 0.5799635E+01 0.1553962E+02 0.3599934E+01
EXPONENTS 0.1013762E+01 0.1553962E+02 0.3599934E+01 0.1013762E+01 0.1553962E+02
EXPONENTS 0.3599934E+01 0.1013762E+01 0.1553962E+02 0.3599934E+01 0.1013762E+01
EXPONENTS 0.2700058E+00 0.2700058E+00 0.2700058E+00 0.2700058E+00 0.8450000E-01
EXPONENTS 0.8450000E-01 0.8450000E-01 0.8450000E-01 0.8000000E+00 0.8000000E+00
EXPONENTS 0.8000000E+00 0.8000000E+00 0.8000000E+00 0.8000000E+00 0.5484672E+04
EXPONENTS 0.8252349E+03 0.1880470E+03 0.5296450E+02 0.1689757E+02 0.5799635E+01
EXPONENTS 0.1553962E+02 0.3599934E+01 0.1013762E+01 0.1553962E+02 0.3599934E+01
EXPONENTS 0.1013762E+01 0.1553962E+02 0.3599934E+01 0.1013762E+01 0.1553962E+02
EXPONENTS 0.3599934E+01 0.1013762E+01 0.2700058E+00 0.2700058E+00 0.2700058E+00
EXPONENTS 0.2700058E+00 0.8450000E-01 0.8450000E-01 0.8450000E-01 0.8450000E-01
EXPONENTS 0.8000000E+00 0.8000000E+00 0.8000000E+00 0.8000000E+00 0.8000000E+00
EXPONENTS 0.8000000E+00 0.1873114E+02 0.2825394E+01 0.6401217E+00 0.1612778E+00
EXPONENTS 0.3600000E-01 0.1100000E+01 0.1100000E+01 0.1100000E+01
This section now tells us what the orbital exponent is for each of these primitives. You can verify this by looking on the basis set exchange to see what the exponents are for 6-31++G** for H, C, and O. Gaussian format has the exponent of each primitive in the first column (note that 6-31g and related basis sets are sometimes written with the label 'SP', which just means you have s and 3 p primitives that all have the same exponent).
Section 5
MO 1 MO 0. OCC NO = 2.0000000 ORB. ENERGY = -20.2999736
-0.12188442E-13 -0.22485295E-13 -0.36298238E-13 -0.47249521E-13 -0.40318102E-13
-0.13920872E-13 -0.41960794E-12 -0.19339692E-12 0.54230514E-12 -0.39273770E-15
-0.30112636E-15 -0.15028316E-15 0.29917662E-03 0.22938966E-03 0.11448152E-03
-0.63478413E-13 -0.48671221E-13 -0.24290350E-13 0.22529127E-12 0.13071387E-15
0.10185809E-03 -0.62728986E-13 0.10023463E-12 -0.29802626E-16 0.15830967E-04
-0.98332270E-14 -0.24693743E-12 -0.14752123E-11 -0.25765489E-12 0.18297189E-14
-0.66615675E-15 0.54705851E-03 0.58494882E+00 0.10766181E+01 0.17421713E+01
0.22901329E+01 0.19642337E+01 0.67160487E+00 -0.91594649E-02 -0.40869354E-02
0.12068775E-01 0.13518265E-14 0.10415094E-14 0.45727874E-15 -0.28829800E-02
-0.22211807E-02 -0.97521795E-03 0.12404677E-02 0.95571350E-03 0.41960970E-03
0.87774840E-03 -0.32212280E-15 0.15512643E-03 -0.10153969E-03 -0.16545660E-03
0.61506469E-16 -0.37903054E-05 -0.37038128E-05 -0.33187344E-02 -0.31410279E-02
-0.33038069E-02 0.74824127E-15 -0.24267011E-15 0.10744751E-03 -0.58494882E+00
-0.10766181E+01 -0.17421713E+01 -0.22901329E+01 -0.19642337E+01 -0.67160487E+00
0.91594649E-02 0.40869354E-02 -0.12068775E-01 0.12737899E-14 0.98138644E-15
0.43088151E-15 -0.28829800E-02 -0.22211807E-02 -0.97521795E-03 -0.12404677E-02
-0.95571350E-03 -0.41960970E-03 -0.87774839E-03 -0.13253444E-15 0.15512643E-03
0.10153969E-03 0.16545660E-03 0.23148336E-16 -0.37903054E-05 0.37038128E-05
0.33187344E-02 0.31410279E-02 0.33038069E-02 -0.14848270E-16 -0.68315079E-15
0.10744751E-03 -0.34702469E-13 -0.58861956E-13 -0.67012256E-13 0.22566017E-13
-0.31113147E-14 0.92067613E-15 -0.20220193E-03 0.19169822E-12
Finally, we have the specification for the MOs; here I just list the first one, but there should be 12 in total to specify all 12 Molecular Orbitals. These specifications list the occupation number and orbital energy, as well as the MO coefficients which tell you how to form the MOs from the primitives.
As you have already seen, this format is a little terse and it can be somewhat unclear what the sections mean at a glance. Gaussian can also produce a newer version in the *.wfx format, which labels each section with a little tag and can be extended to include additional wavefunction features.
