mat files contain data saved in Matlab's proprietary format. How to read these files in Python depends on the version of Matlab used to save them, up to 7.1 or greater.
Here are exemples of how to read two variables lat and lon from a mat file called "test.mat".
Matlab up to 7.1
mat files created with Matlab up to version 7.1 can be read using the mio module part of scipy.io. Reading structures (and arrays of structures) is supported, elements are accessed with the same syntax as in Matlab: after reading a structure called e.g. struct, its lat element can be obtained with struct.lat, or struct.__getattribute__('lat') if the element name comes from a string.
Matlab 7.3 and greater
Beginning at release 7.3 of Matlab, mat files are actually saved using the HDF5 format by default (except if you use the -vX flag at save time, see help save in Matlab). These files can be read in Python using, for instance, the PyTables or h5py package. Reading Matlab structures in mat files does not seem supported at this point.