碍事 has two main uses: physically blocking or hindering (e.g. a piece of furniture in the way), and, often in negative sentences like 不碍事, meaning 'to not matter' or 'to be of no consequence.' It can also function as an adjective describing something inconvenient or obstructive. The negative form 不碍事 is a common polite way to reassure someone that there's no problem.