You are buying Ether which could be a token, a portion of the token or tokens from the Ethereum blockchain. A blockchain consists of combined blocks of transactions of issued tokens between addresses.
A token in a blockchain is immutable that is, a token cannot be duplicated, replicated or mutated in any form in which case if it is added from an external source, the network shall decline it as it would fail the proof of work test.
Tokens issued from a blockchain are of no value unless they can be spent ( sent to another account ) that is a token within any economy is useful only as it creates progressive value on being circulated within. In this case, Tokens are said to be burnt if they cannot be spent. Burnt tokens, relatively increase the value of tokens that are available for circulation within the network.
Ethereum plans on employing a proof of stake methodology from a proof of work methodology in validating the previous transactions.
Ethereum employs a proof of stake methodology while mining ( arranging transactions into blocks within the blockchain ) which means that, everybody has an integral portion of the tokens issued by the blockchain or rather everyone holding Ethereum has a stake in the Ethereum Economy.
When one is said to have bought Ethereum, they are said to have a stake in the total number of tokens(Ether) issued by the blockchain similar to how one would own 10% of company X if a person owns 10 of 100 is the total stock issued. Ethereum works in a similar manner to prevent a 51% attack since a person trying to execute this manner of an attack would be required to own 51% of the total Ether issued thus granting them the ability to change the immediately previous transaction if they did make it.
Ethereum does not have a capped limit which implies that your stake within the Ethereum economy is decreasing every single day as the blockchain issues more and more Ether to the network.
Ether is also used as gas while executing smart contracts.
To summarize, You are buying Ether, a stake of the total amount of Ethereum issued and ability to execute a smart contract when you buy Ethereum.
Of course, A lot would depend on the amount of Ether you buy as well for there is a mighty huge difference between the amount of Ether to be in one’s possession to execute a 51% attack and the amount of Ether in the form of gas required to execute a contract.
Theproject does a great job of explaining Ethereum as well.