Politics is often drawn as a line. The centre is the middle: not a huge change, not a hard push for a new system. Left-of-centre means you sit on that line a little toward the left. You tend to want more help from the state for people with less money, stronger public services, and more rights for workers — but you are not at the far left, and you are not calling yourself a communist. Parties, newspapers, and people all get this label. It is a calm, slightly formal newspaper word. The spelling centre is British; American English writes left-of-center. The hyphens are normal when the whole phrase describes a noun (a left-of-centre party). Though actually, “left” and “centre” do not point to the same list of beliefs in every country, so the word tells you a direction on a map, not a fixed programme.