'right' is used as an intensifier to mean 'to the furthest or most complete degree'.
Other examples are 'on the edge', 'right on the edge'.
'The table is next to the bed', 'The table is right next to the bed.'
'I'll be back', 'I'll be right back'.
We often say 'right away', which is the same as 'straight away' or 'immediately'.
We use 'right' in this way a lot for time and also for location.