Hi "keets"
합니다 is a polite present tense form of the
'하다'(to do) verb
It's a bit weird, but in the case of saying 'Happy Birthday?' 생일 축하 합니다 it translates literally something like this 생일(birthday) 축하(congratulation) 합니다(doing) e.g. 'I am congratulating you on your birthday'
A simpler example: 'I am woking' 일을 합니다 literally '(일)work (합니다)doing'
Some variants:
하십니다 - used with respect particle "시" to describe current continuing actions of a social superior -- never used to describe one's own actions
합니다 - polite present tense of 'doing'
한다 -informal present tense of 'doing'