"Meaning - Don't be ungrateful when you receive a gift.
...category of phrases called proverbs, that is,
'short and expressive sayings, in common use,
which are recognized as conveying some accepted truth or useful advice'.
The phrase is often expressed as 'never look a gift horse in the mouth'.
As horses age their teeth begin to project further forward each year
and so their age can be estimated by checking how prominent the teeth are.
This incidentally is also the source of another teeth/age related phrase
- long in the tooth.
The advice given in the 'don't look...' proverb is: when given a present,
be grateful for your good fortune
and don't look for more by examining it to assess its value.