What are the coupling constants (#J#)?

The coupling constant #J# is pretty much the peak-to-peak distance, usually reported in #"Hz"#. Matching it up with other nearly-identical coupling constants elsewhere in the spectrum usually tells you which protons are near which others.

For example:

Peak Data:
#"Hz"" "" " "" " ppm"" ""Intensity"#

Proton A:
#"371.56"" ""4.149"" ""24"#
#"365.38"" ""4.080"" ""56"#
#"359.25"" ""4.012"" ""72"#
#"353.13"" ""3.943"" ""60"#
#"347.06"" ""3.876"" ""28"#

Proton B:
#"193.00"" ""2.155"" ""335"#

Proton C:
#"110.44"" ""1.234"" ""1000"#
#"108.19"" ""1.209"" ""27"#
#"104.31"" ""1.165"" ""939"#
#"102.06"" ""1.140"" ""25"#

What is shown here for proton A is that #"4.008 ppm"# is the average chemical shift of the 1-4-6-4-1 pattern (according to Pascal's triangle) from the rightmost peak to the leftmost peak, and the entire signal there has multiple peaks. The peaks split like so:

1 #-># 1-1 #-># 1-2-1 #-># 1-3-3-1 #-># 1-4-6-4-1

It is not visible in this zoom, but the distance between each peak is roughly identical. This distance is the numerical equivalent of the coupling constant #J# in #"Hz"#. For proton A:

#4.149 - 4.080 = "0.069 ppm"#
#4.080 - 4.012 = "0.068 ppm"#
#4.012 - 3.943 = "0.069 ppm"#
#3.943 - 3.876 = "0.067 ppm"#

Interestingly enough, if you look at protons C at the averaged #"1.200 ppm"#, you would also see that that doublet has the same #J# value (ideally that doublet should have both peaks at identical intensities too, but the shimming was not perfect, so they are a bit off). For proton C:

#1.234 - 1.165 = "0.068 ppm"#

From the identical (or nearly-identical) coupling constant, you can determine which protons are "communicating" with each other and thus which protons they neighbor.

If you take this number and multiply it by the #"MHz"# of your NMR, you get the coupling constant in #"Hz"#. So, if your NMR's magnetic field frequency is #"89.56 MHz"# (like for this particular spectrum), then:

#"0.068 ppm" * "89.56 MHz"#

# = 0.068 ("Hz")/("MHz") * "89.56 MHz"#

#= color(blue)"6.09 Hz"#

Indeed, for proton C, #110.44 - 104.31 = "6.13 Hz" ~~ "6.09 Hz"#.

Therefore, without seeing the structure of the analyzed molecule, you can still figure out that proton A and protons C are coupling/"communicating" with each other.