If you’re at a loose end, why not read this word grammar article by Tim Bowen?
The adjective loose is most frequently used to mean ‘not fixed in position’, as in ‘a loose floorboard’ or ‘a loose tooth’, or to mean the opposite of tight, as in ‘He was wearing a loose cotton shirt’.
It can also be used to mean ‘not exactly accurate in every detail’, as in ‘This is a loose translation of the letter’ and ‘not strictly organized or official’, as in ‘We’ve got a loose arrangement for looking after each other’s children’.
Loose is also used in a number of expressions. If you break loose, for example, you stop being connected with something or influenced by someone or something, as in ‘It is a country that is trying to break loose from its bloody recent past’.
If you let someone loose on something, you let them do what they want to do without watching or controlling them, as in ‘Whatever you do, don’t let the children loose on the paints’.
If someone has a screw loose, they are slightly eccentric or crazy and if you find yourself at a loose end, you have nothing in particular to do, as in ‘Why don’t you drop by one day if you’re at a loose end?’
A loose cannon is a member of a group or team who tends to do unexpected things that could cause problems for the other members, as in ‘She was widely regarded as something of a political loose cannon’.
Loose can also function as a noun but only in the very restricted phrase on the loose. If a dangerous person or animal is on the loose, they have escaped from where they were being kept, as in ‘There are persistent rumours that a puma is on the loose in Gloucestershire’.