Plug and Play games are videogames that do not need a console to play. Although they're mostly considered as toys, they usually package classic games into each unit. Many of these games are old console and arcade classics (Namco, Atari, and Colecovision are examples). There are some original plug and play games, but are mostly kid brands (like Spiderman and Spongebob Squarepants). The Most Common maker of these games are Jakks Pacific.
Regular Plug and Play TV units are controllers with A/V cables connected to it. All the games are programmed inside the controller itself so there is no need to have any consoles in order to play the games. The A/V cable connects directly to the TV. Each unit has a power switch and a control layout which is appropriate for the games you're playing (Atari 2600 Unit is shapped like an Atari 2600 controller, Namco Units have a joystick with arcade-style buttons). If a unit has more than one game, a menu will pop up, letting you decide which game you want to play. If you want to play another game, you'll have to reset the unit to go back to the menu or turn off the unit and turn it back on again.
Some of these units can also be handhelds. For example, VG Pocket MAX has a feature which lets you connect to your TV using A/V cables. Also, the Sony PSP 2000/3000 lets you connect to your TV using A/V cables.
Although Plug and Play games are convenient and cheap, they have a lot of issues with their design. Due to their cheap nature, these units can break easily. the controllers can be messed up by having buttons stick, the joysticks would be off-centered, and the d-pads will not function well. Also, if you drop the controllers, you can mess up with the games. Pink pixels can pop on the screen blocking your view. It can also mess with the sound.
Due to their cheap nature, these units are not true alternatives to consoles. Many of the games do not play as well as their original counterparts (botched sound, graphics, etc.). Also many of the games are cheaply made and are made to last a short time.