I take it that you've been reading Enid Blyton again? Or other British writers from the mid-twentieth century? 'Jolly well' is an adverbial phrase used to add emphasis, sometimes indicating annoyance or irritation. For example:
'Where's my book gone?'
'Johnny borrowed it, and .. um .. I think he's lost it'.
'Lost it? Well, he can jolly well find it again!'
This is quite old-fashioned, from the days when swearing was less permissible than it is today. A less 'Enid Blyton-ish' way of say this might be the equally British but rather less polite 'He can bloody well find it' or the more American 'He can darn/damn well find it'. Whatever phrase you use, it's just there to add emphasis.
The comment means 'He'd better find it!' , but it's stronger than that. The implication is 'He'd better find it ... because if he doesn't, he's going to be in trouble'.
Do we still use 'jolly well' in this way nowadays? Sometimes. I do, anyway. It's a good way of being emphatic without actually swearing.