In order to make sure elections are trustworthy, votes are kept private. This means that who you voted for is secret. Nobody else should be able to figure out who you voted for. Even you, the voter, should not have a record of how you voted.
Keeping votes private protects voters from coercion. If votes are revealed, then that can be taken advantage of in order to influence how people vote, thus potentially changing the outcome of the election. Secret votes protect voters from tactics like bribery and intimidation that might otherwise influence them to vote differently than they want to. Even giving voters a record of how they voted can leave them vulnerable to those tactics, because it would possible for the voters to be forced to show someone else that record.
With paper ballots, privacy means that ballots have no indication on them of who cast them. Electronic voting takes its own steps to ensure that there is not a connection between an electronic ballot and the person who casts it. No personal information is recorded with your ballot when you cast your vote. Even information such as the times when ballots are cast should be stored separately from the contents of the ballots themselves, so that attackers cannot use other sources such as security cameras to connect the ballot to the person who cast it.
Another security measure that keeps your vote private is encryption. Encrypting ballots prevents your vote from being viewed or changed by someone who is trying to influence an election. When your ballot is encrypted, it cannot be decoded by anyone who is not allowed to do so. This way, even if someone malicious does manage to find an electronic copy of your ballot, they will be unable to tell who you voted for. For an example of how one electronic voting system encrypts votes, see our page on Helios cryptography.