3 Answers

Sincere:  sin·cere.  adj \sin-?sir, s?n-\  sin·cer·ersin·cer·est

Definition of SINCERE

1. a. free of dissimulation : honest <a sincere interest>

    b: free from adulteration : pure <a sincere doctrine> <sincere wine>

2: marked by genuineness : true

Examples of SINCERE

He sounded sincere in his promises.She seemed sincere in her commitment to finish school.She has a sincere interest in painting.He showed a sincere concern for her health.He made a sincere attempt to quit smoking.Please accept our sincere thanks.

Origin of SINCERE

Middle French, from Latin sincerus whole, pure, genuine, probably from sem- one + -cerus (akin to Latin crescere to grow) — more at same, crescentFirst Known Use: 1533

Synonyms: heartfelt, unfeigned

http://www.merriam-webster.com/dictionary/sincere  Source

sin·cere   [sin-seer] 
adjective, -cer·er, -cer·est.
1.
free of deceit, hypocrisy, or falseness; earnest: a sincere apology.
2.
genuine; real: a sincere effort to improve; a sincere friend.
3.
pure; unmixed; unadulterated.
4.
Obsolete . sound; unimpaired.

http://dictionary.reference.com/browse/sincere

Simply put, SINCERE means that you say what you mean, you do what you feel is right, and you don't BS people.  Some people seem sincere (honest) but are not. Unfortunately, we sometimes figure this out too late and end up hurt by their INsincerity.