"The Punisher is a great 2 player co-op game on MAME."
"MAME is one of the greatest emulators made for older games."
In plain English, if you have a copy of an arcade game, you can (theoretically) play it in your PC using MAME. Arcade games are usually stored in ROM chips, so such a copy is called a ROM image or simply "rom". New arcade systems use harddisks, so in that case you have a copy of the harddisk, usually called a "chd" file. Mimicing the behavior of an arcade system is done by translating the instructions from the "machine language" of the arcade system to the "machine language" your PC uses.
The only catch is that, as mentioned, MAME has huge overhead and thus is slow. Even if the original arcade system run at a measly 30Mhz, your 2-3GHz CPU may struggle to cope.
MAME developers claim that such overhead is neccessary to make the result as faithfull to the original as possible, but truth is, MAME could be faster without losing any accuracy, for example skipping step-by-step emulation when not neccessary.
But since the stated goal of the MAME project is to preserve the arcade legacy for future generations and not make arcade games playable right now, theoretically the project has achieved it's goal.
On a practical level, 2D games will run fine, but for 3D games (even early ones), you 'd better look elsewhere, such as Nebula, Kawaks, Calice, Zinc, FinalBurn Alpha, VivaNonno, Raine and other fast emulators.
One more detail: Use MAMEUI for Windows, and SDLMAME for OS X.
I can't believe MAME needs a 3GHz CPU to run Ridge Racer 1 in my PC. The original arcade system had a 24.5Mhz CPU!