The 9 eggs category is one of the four main routes offered in Limbo. It's most comparable to the any% normal route, the only difference being players go out of their way to collect the 9 hidden eggs along the way. An egg will start to glow as you approach it, and stepping on and triggering a "cracking" sound will signify that the egg was collected.
There are a total of 11 eggs in the game, but one is at the end of the hard route, which we never see. The other is in the candle room before the hard route, but once you collect it, it never respawns. The nine eggs in this route will always respawn after dying, loading a chapter, or starting a new game. If you die after collecting an egg and hence respawn the egg, you do not have to collect it again.