It's the amount of people one person could infect. If it's above 1 the virus will grow exponentially, if it's below 1 it'll gradually die out due to lack of people infecting each other.
For example if the R number is 3 then each person who gets it will pass it on to 3 other people, if it's 1 then each person will pass it on to 1 other person. So if it's less than 1 then each person will pass it to "less" than one other person so it doesn't spread as much and dies.
Interestingly, left unchecked, measles has an R number of 15