Open primary
In politics, an open primary is a primary election in which a voter is not required to be formally affiliated with a political party prior to participation.
In most cases, the voter simply decides in which primary election to participate (Republican or Democrat; third parties do not use primaries) and does so at the polls. In other cases, a voter can decide to "change" parties at the time s/he votes.
Generally a voter participating in a primary election cannot then participate in a third party's convention later, and may also not be able to sign a nominating petition for a third party or independent candidate (this is the rule in Texas, for example).
It is believed by some that open primaries allow Democrats and liberal independents to influence Republican primaries by electing the weakest and least popular candidate, thus giving liberals and Democrats an advantage come the general election.