Here's what Microsemi said so far. (I'll probably merge the specific files into Brian Drummond's answer and keep the directory information.)
When you create a new project in the Libero SoC it automatically
creates new directories and project files. Your project directory
contains all of your local project files. If you import files from
outside your current project, the files must be copied into your local
project folder.
component directory - Stores your SmartDesign components (SDB and CXF
files) for your created Libero SoC project.
constraint directory -
All your constraint files (SDC, PDC). These are the input files which
are used in Synthesis and Place and Route.
designer directory - ADB
files (Microsemi Designer project files), -_ba.SDF, _ba.v(hd), STP,
TCL (used to run designer), impl.prj_des (local project file relative
to revision), designer.log (logfile)
*adb is the output
hdl directory - all hdl sources. *.vhd if VHDL, *.v and *.h if Verilog.
All these are the input files.
phy_synthesis directory - _palace.edn,
palace_top.rpt (palace logfile) and other files generated by PALACE
simulation directory - meminit.dat, modelsim.ini files
smartgen
directory - GEN files and LOG files from configured generated cores
synthesis directory - *.edn, *_syn.prj (Synplify log file), *.psp
(Precision project file), *.srr (Synplify logfile), precision.log
(Precision logfile), *.tcl (used to run synthesis)
*.edn is the Output file.
Also
*.cfg This captures information about the settings that were specified for the system
*.bfm BFM is a stimulus file. These files are provide to Simulation tool.
*.def Discontinued Programming file. Output file from flashpoint.
*.gen Output netlist file from the generated cores
*.ipd Programming file
*.loc lets you know the location of the Logic inside the FPGA.
From http://soc.microsemi.com/kb/article.aspx?id=SL5622 some programing files are
*.spi Auto Programming, also Cortex-M3 ISP, and In Application Programming (IAP)
*.stp, .ipd,.dat JTAG programming. Also SPI Slave Programming