Banks do not borrow money from the central bank. Generally they deposit excess reserves with the central bank and are remunerated on a daily basis at the deposit rate (ECB depo rate, BOE base rate, FED funds rate).
Central banks do have standing facilities to loan money to banks but these are generally expensive and meant as a last resort. They can also give bad impressions on the credit worthiness of the institution if it consistently needs to utilise these measures.
OIS is the overnight indexed swap rate. It is compiled differently in different currencies. In GBP it represents the weighted average of interbank overnight cash transactions reported through a series of brokers over 25mm (don't quote these exact details). In EUR it is compiled by the ECB by aggregating a series of loan rates provided by a selected group of large banks to other banks.
These systematic differences and other factors determine the precise relationship between OIS and the central bank deposit rate in any given currency (look at DKK for a really wacky relationship)