what is this and why is it disconected?

ok
been having a few problems
the alarm keeps going off
battery is regularly flat
alarm people have had a look
had a new battery fitted
seemed to fix problem
3 days later battery flat
took it to subaru garage
they could not find fault
got it back working fine
had a look under the bonnet
this (see picture) was disconected
subaru said they didnt move it
alarm people said they didnt shift it
son said he hasnt moved it
and i know i have not removed it
so i pluged it back in , but what is it

thanks in advance
Norman