MRR stands for Monthly Recurring Revenue, which is the total amount of revenue that a company expects to bill on a monthly basis. It's the lifeblood of any SaaS business and one of the first metrics most SaaS companies are asked for.
MRR is what makes SaaS such a brilliant business model – it's vastly more predictable than most revenue streams generated by other business types. Most businesses require constant marketing activity to keep one customer paying month over month (think about supermarket loyalty programs) and there's no guarantee at all that they'll work. With SaaS businesses, monthly recurring revenue is the default method of revenue generation, which is why SaaS businesses are normally valued in multiples of ecommerce businesses (for example).
Accounting purists suggest that when you calculate ARR, it should only be done in relation to annual terms, so the minimum contract size has to be one year - but there's no reason you can't do this the other way around, to get a handle on your business' month-to-month performance fluctuations.
To get a better understanding of MRR, try: