In a piece of music I'm learning, there is a percentage sign taking up a whole bar, which I know means repeat the previous bar. However there is another sign in the following bar, yet this one has a three in brackets above it. What does this mean?
The percent sign is actually known as a simile mark. Like you said it just means to repeat the previous measure. The 3 in brackets is slightly informal and is telling you this is the 3rd measure repeat so it is no different then the previous simile repeats, it's just telling you how many times you have repeated so far. Sibelius seems to put them in by default.
Simile markings will tell you how many measures (not how many times) to repeat in a block. This image, from wikipedia, shows the number of slashes indicating the number of measures.
As Dom wrote, little numbers above the markings are there to help musicians keep track of their position.