The attacker budget message in the iPhone app is there to give you an estimation of the password's strength.
The assumption here is that if the website of your account got hacked and a passwords database based on SHA-1 hashes was leaked within the hacker community or publicly; then a person would be able to try and hack your account's password for that site. In this event, it's important that you use complex passwords to protect yourself. Master Password offers several types of passwords, each with varying complexity.
If the meter says "9 months", and the budget is set to Regular, then an attack of a private individual on your password based on a password database leak of your site would require the individual to run a dedicated exhaustive search with his full hardware capacity on your password, 24/7, for 9 months, before he'd be able to unscrable your password from it.