I've searched online dictionaries but I couldn't find the meaning of
be from money.
The example is:
To anyone who doesn’t know who Matthew is, they just come across as a well-heeled, successful couple. But Matthew is from money, and lots of it.
The full text is here:
She gets dressed quickly in a simple but elegantly cut dress. Everything she wears flatters her. Genetics has been kind to her, and she now has the money to make the most of what she’s been given. Matthew is a warm, generous man, and she’s very much in love with him. Of course, the money doesn’t hurt. She thinks often of how lucky she is, of how awful it must be for most women—to marry and have children on a budget. She’s well aware that she and Matthew have a charmed life. She’s not going to apologize for it. But she’s certainly not going to rub anyone’s nose in it either. She knows what it’s like to want—to want desperately—things that you can’t have. To anyone who doesn’t know who Matthew is, they just come across as a well-heeled, successful couple. But Matthew is from money, and lots of it.
Also, does the word "but" in "But Matthew is from money..." suggest that maybe he is personally not rich?