It means that there is a publicly announced transaction that everyone is aware of that credits your account with 0.01 BTC from some other account. It is digitally signed by the owner of the source account, so everyone knows that they agreed to pay you the 0.01 BTC.

There are no BTCs really, just transactions. Your BTCs are just transactions to you from others. Transactions that you own can be split or combined when signing then over to other accounts.

The question originates from the thread The legal definition of bitcoins (translated from Russian), where they're trying to determine the legal definition of bitcoins.

The same topic has been discussed in English in multiple threads, including one titled Money Transfer Regulations.

I'm not a lawyer, but to the best of my knowledge, from a general legal perspective, bitcoins are digital goods, элeктpoнныe тoвapы. But if a business is trading large amounts of money in and out, they would still need to follow financial regulations, including but not limited to KYC (Know Your Customer) regulations, to discourage money laundering.