Hidden is a special status for players. When you are hidden, you cannot be attacked.The only exception is that you can be attacked during clan attacks.
However, this also means you cannot attack. Being hidden also restricts most movements, according to your species.

You can HIDE and UNHIDE using this button in the Menu:

Different species hide in different ways.

Marines:

Hide by going back to their Headquarters, HQ. They are invulnerable in there. Hiding is free for Marines, but it restricts every other types of movement. When hidden, Marines cannot attack, visit Shops, visit the Forum, they mostly cant do anything until they come out of hiding.
A hidden Marine will display this icon in his status bar:

Aliens:

Hide by crawling on walls. This allows them to hide up on the ceiling or inside vents. Wallwalking is for free, but it restricts the Aliens movements to the maximum. The only area a hidden Alien can visit is the PM box.

Crawling is represented in your status bar by this icon:

Predators:

Hide by cloaking. This is a special type of hiding, and is not for free. When cloaked this icon will appear in his status bar:

Read more about: cloaking