Thanks for your interesting question, Bjorn.
The term comes from the House of Lords in the British Parliament where a number of benches are positioned between the government and opposition benches.
If you are elected to Parliament, but not a member of the government or opposition parties, you sit on the crossbench. This is where independent members and senators and those elected from minor parties are located.
Crossbench members and senators represent an electorate, state or territory in the same way as those who belong to the government or opposition parties. They take part in debate on government bills—proposed laws—and can introduce their own bills called private member’s or private senator’s bills.
While members of major parties usually vote together to support or reject an idea, independent and minor party members can make up their own mind as to how they will vote. The result is that some of the crossbench may vote with the government and others with the opposition.