Based on Ash's actions in the early part of the film we can ascertain that the Science Officer is responsible for a range of sciencey things, notably the safety and wellbeing of their very large and expensive refinery as well as orbital mechanics for the Nostromo.
The tug and refinery rotated, performing a massive pirouette in the vastness of space. Light appeared at the stern of the tug as her secondary engines fired briefly.
'Equatorial orbit nailed,' declared Ash. Below them, the miniature world rotated unconcernedly.
'Give me an EG pressure reading.'
Ash examined gauges, spoke without turning to face Dallas. 'Three point four five en slash em squared. . . About five psia, sir.'
'Shout if it changes.'
'You worried about redundancy management disabling CMGS control when we're busy elsewhere?'
'Yeah.'
'CMG control is inhibited via DAS/DCS. We'll augment with TACS and monitor through ATMDG land computer interface. Feel better now?'
'A lot.'
Alien: Official Novelisation
His console contains information about the ship's atmosphere, ensuring that it remains breathable and uncontaminated.
Ash studied his own console. Along with the others, it was
independently powered in the event of a massive energy failure such as
they were presently experiencing. 'Air in all compartments shows no
sign of contamination from outside atmosphere. I think we're still
tight, sir.'
He also supports Captain Dallas in deciphering the distress signal.
'The emergency lies elsewhere - specifically, in the unlisted system
we've recently entered. We should be closing on the particular planet
concerned right now.' He glanced at Ash, who rewarded him with a
confirming nod. 'We've picked up a transmission from another source.
It's garbled and apparently took Mother some time to puzzle out, but
it's definitely a distress signal.'
He also acts as the ship's primary medic after an injury occurs, although he goes to pains to indicate that he's not a doctor.
'Long-term prognosis?'
The science officer looked hesitant. 'I'm not a medical officer. The Nostromo isn't big enough to rate one.'
'Or important enough. I know that. But you're the closest thing we've got.