Agar-Agar is a gel forming ingredient, extracted from seaweed, that is used to make petri dish media.
You could use gelatin but mycelium will digest gelatin and you'll be left with a useless goopy mess. Agar-Agar enables mycelium to grow on a solid plate surface so that you can cut wedges out, and use them to inoculate things. The solid 2-dimensional media also makes for good visual indication that your culture is either clean or not clean. Agar being on a 2d surface, rather than 3d(cake or grain jar) or in liquid, allows for easy salvaging of most contamination problems before it's ever a problem. In some cases, if a contaminant appears on a dish, you can re-capture mycelium. Then use that clean wedge to create a new 100% clean dish, and entirely save a culture.
Agar-Agar itself is not nutritious. This is confusing as "agar" refers to the ingredient in "agar". Agar sometimes means the whole media prepared with agar(the gel forming powder) and then nutrition and water.
"I use agar and I love it.
The idea is that you are growing on a 2-dimensional plane (the agar surface) instead of a 3-dimensional substrate (PF cake, grain in jars, etc.) On the flat surface of the agar, contaminates cannot hide from you. You can isolate clean mycelium from dirty prints. You can also clone fragments of tissue, do breeding experiments by isolating single spores and select and propagate specific isolates. Agar is also often used for the storage of favored strains. Just pop them in the fridge for several months.
Agar culture is just a more powerful and precise way of doing things. If you like control, agar is for you. If not, just inject your spores and cross your fingers ;) "Agar Portal (2017 up to date agar links)
Bod's comprehensive agar TEK
Short and simple pour agar TEK
You may need to log in at the forums to get the whole experience. The first link contains a more comprehensive list of Agar resources.