Lumens is the native currency of the stellar network. It’s used to incentivise the work necessary to make the network function. In the words of the developers, the Stellar network is too easy to use, which means that there needs to be some small barrier to entry to prevent the ledger from becoming clogged with spam.
Each account in the network must therefore have a minimum balance of one lumen, and a transaction fee of a small fraction of a lumen. This prevents bad behaviour from spambots, while still keeping things accessible for everyone else. Rather than using an existing currency, like the dollar, the lumen was created, just to keep things neutral and free from external control.