Sometimes, a handshake is not just a handshake. When you look at the sleeves of these clasped hands, pictured on the gravestone of M. J. Butler, you can see that one seems to be that of a woman and one of a man. This tends to symbolize a good marriage.
On the other hand, if the sleeves seem to be gender neutral, it could symbolize the hand of God welcoming the soul of the dead into the heavenly kingdom.
Another interesting thing in this symbol is that the index finger on one or both hands might be extended. This indicates that one or both of the couple was a member of the Masonic Lodge.