"Net 30" is shorthand for payment due 30 calendar days after the invoice date. Net 7, Net 14 and Net 60 work the same way with a different number of days.
"Net" originally meant the full (net) amount was due, with no early-payment discount. You will sometimes see it combined with a discount, such as "2/10 Net 30": 2% off if paid within 10 days, otherwise the full amount in 30.
Weekends and bank holidays count, unless your contract says business days.
Example
An invoice dated 1 March on Net 30 terms is due on 31 March.