Bitcoin is a collection of computers, or nodes, that all run Bitcoin's code and store its blockchain. A blockchain can be thought of as a collection of blocks. In each block is a collection of transactions. Because all these computers running the blockchain have the same list of blocks and transactions and can transparently see these new blocks being filled with new Bitcoin transactions, no one can cheat the system. Anyone, whether they run a Bitcoin "node" or not, can see these transactions occurring live. In order to achieve a nefarious act, a bad actor would need to operate 51% of the computing power that makes up Bitcoin. Bitcoin has around 47,000 nodes as of May 2020 and this number is growing, making such an attack quite unlikely.
In the event that an attack was to happen, the Bitcoin nodes, or the people who take part in the Bitcoin network with their computer, would likely fork to a new blockchain making the effort the bad actor put forth to achieve the attack a waste.
Bitcoin is a type of cryptocurrency. Balances of Bitcoin tokens are kept using public and private "keys," which are long strings of numbers and letters linked through the mathematical encryption algorithm that was used to create them. The public key (comparable to a bank account number) serves as the address which is published to the world and to which others may send bitcoins. The private key (comparable to an ATM PIN) is meant to be a guarded secret and only used to authorize Bitcoin transmissions. Bitcoin keys should not be confused with a Bitcoin wallet, which is a physical or digital device which facilitates the trading of Bitcoin and allows users to track ownership of coins. The term "wallet" is a bit misleading, as Bitcoin's decentralized nature means that it is never stored "in" a wallet, but rather decentrally on a blockchain.