An inflation operation runs each week, increasing the supply of lumens by 1% annually.
The Stellar network has a built-in, fixed, small inflation mechanism. Anyone can submit the inflation operation to the network each week, which then triggers inflation.
The network will only accept the inflation operation if it has been one week or more since the last time the operation ran.
Fees on the Stellar network are recycled back into circulation through this inflation mechanism, which, on top of the recycled fees, inflates the number of lumens by 1% annually.
Inflation is issued weekly at 1% / 52 weeks = ~0.019%, plus the transactions fees collected over the past week.
Anyone who holds lumens can vote on which account should receive inflation - each lumen equals one vote. The network distributes inflation to any account that gets over 0.05% of the votes, in proportion to the number of votes each account receives.
"Voting is weighted according to the number of lumens the voting account holds." - Stellar Dev Docs
Because the value of the asset slowly increases as supply decreases, deflation causes people to be more likely to hold a currency instead of use it, and - vice versa - a high inflation rate incentivizes people to quickly spend a currency. A nominal (small) inflation rate like 1% provides a good middle ground and replaces the lumens that are inevitably lost when various account owners lose their secret seed.
The small 1% inflation rate creates a more stable supply of lumens over the long term.