The meaning of SEEMS and APPEARS are very similar and in many cases are used interchangeably. They do have slightly different meanings and connotations though.
APPEARS means to come into view and is more commonly used for something that is observable. In your sentence HE APPEARS TO BE A GOOD PERSON, one would assume that the statement is based upon seeing things this person does. He helps old ladies across the street, smiles at everyone, etc.
SEEMS means to give an impression. It is commonly used more for subjective opinions of the viewer and may not be based upon anything observable. So when saying HE SEEMS TO BE A GOOD PERSON, that statement may be based upon nothing more than a hunch.
With your sentence, it isn't necessarily an easy distinction to be seen. But try it on this sentence: THE BEACH APPEARED SAD. This sentence seems a bit odd. There isn't really any visible aspect of a beach which could be construed as sad. THE BEACH SEEMED SAD, however, makes more sense. In this sentence the speaker is simply saying that the beach seems like a sad place to them. It is about what they feel, not what they see.
Here is another example. Compare THE THEATER APPEARED EMPTY with THE THEATER SEEMED EMPTY. In the first, the meaning would be taken as a visible observation and the statement would suggest that the theater literally was empty. No one was in it. In the second, however, it just is perceived to be empty. It may not be, maybe everyone is just really quiet, or far away.