'appear to' is similar to 'seems' or 'looks like'. For example, if you say 'The computer appears to be broken', it means that it isn't working, and so you think that it's probably broken. You're not 100% sure, but the evidence suggests that this is the case.

Is I say: «It seems to be older than it looks» it helps you ?

There appears to be a storm coming. It appears that the stock market is in a bull market. There appears to be an opportunity for me here. There appears to be many people signing up for this event. There appears to be little that we can do about it now. There appears to be a solution by getting the opposing parties to discuss possible compromises. There appears to be no references to this 40 year old math book on the Internet, and that is why I will probably never find a used copy to buy. There appears to be many tutors and teachers using the Italki forums.