The Personal Safe is a special chest added by the Industrial Craft 2 mod. It can only be opened by the first player to open the safe. It's blast resistance is high enough that it is completely impossible to destroy with TNT, as it exceeds the blast resistance of bedrock.
The Personal Safe is also unbreakable by a player who is not in Creative Mode, but a player in Creative Mode can open and destroy these chests. Items CANNOT be transported from things like BuildCraft Pipes into or out of the chests.
Note: that as of Tekkit Lite, the Personal Safe does not open upward like a Chest, but rather opens forward like a swinging door. This is not reflected in the image.