For most employers it literally means what it says. The ability to be able to check you have been where you say you’ve been.
However, for the unemployed returning to work – this isn’t strictly the case. Some people won’t sign on for benefits immediately they become unemployed through pride amongst others things. The thinking can be ‘I’ll find another job in no time. It’s not worth signing on’. Or perhaps some may choose to spend some savings/redundancy on travelling.
It’s worth remembering for some employers a ‘checkable history’ actually means ‘in paid employment or in receipt of benefits’. Any gaps won’t be accepted.
It’s good to check the detail when going for a new role or what things actually mean. Don’t get caught out!