Playing PS2 Games will vary by PlayStation 3 model,as early Fat model have full PS2 Hardware, later revisions went to a partial software / hardware emulation to eventually a 100% software emulations. All PS3 models once jailbroken does have the ability to run PS2 Games via the firmware's ps2_netemu.
Supported Formats (ps2_netemu.self)
ISO, BIN / CUE, BIN.ENC
Supported Location:
ps2_netemu: Place your PS2 ISO images in the /PS2ISO folder on the PS3's internal HDD only
PS2 Emulation
ps2_emu.self - CECH-A/B models use ps2_emu.self able to use built-in PS2 hardware (EE/GS/Rambus memory), and has the best compatibility
ps2_gxemu.self - CECH-C/E models use ps2_gxemu, this emulator use physical Graphic Synthesizer found in this ps3 model, but Emotion Engine is fully emulated here, also there is no Rambus memory
ps2_softemu.self- Sony switched to a 100% Software based PS2 Emulator and this emulator was strongly based off ps2_gxemu in the remaining PS3 FAT models that went into production
ps2_netemu.self - This emulator is used for the "PS2 Classic" ,This version of the emu like ps2_softemu is a 100% software emulation, This is the only version that does not have any physical CDVD disc reading capabilities. This is the only emulators' listed that can be used on Slim / SuperSlim PS3 models.
Additional Notes
Some PS2 Games may require a CONFIG (to be playable or improve emulation)
PS2 ISOs on OFW BC Consoles via Swap Magic (CECH-A - CECH-E)
"Swap Magic is a boot disc from the PS2 scene which allows you to run PS2 backups and homebrew content on a PS3 with any version of OFW. This includes the ability to use OPL and play games from USB or SMB, though FMV and heavy loading games may stutter.
Swap Magic only works on CECH-A through CECH-E consoles'