Contracts have 2 ** 256 32-byte storage slots available to store data in. This can be thought of as each contract having it's own database. Can all nodes in a blockchain network access to smart contract's storage space ?
Any node in the network can read this data but only your smart contract can add/update/delete it.
Only you smart contract is able to alter this storage!
The functions you have in your contract define the conditions under which this storage can be changed.