The two-handed handshake is when somebody shakes your right hand with his, while holding the back of your right hand with his left hand, or alternately holding onto your wrist or forearm while shaking hands.
What message do you get if:
Somebody you’ve just met for the first time greets you with a two-handed handshake?
Somebody you met once before who gave you a standard vanilla handshake and you’ve had no real interaction with him since then, now gives you a hearty two-handed handshake on the second meeting?
Somebody you met once before who you’ve since been working with off and on via e-mail or other interoffice communications, on the second meeting gives you a warm hearty two-handed handshake?
Assume 100% business situations for all above meetings; IOW none of the initial or subsequent contact was after work or in any sort of relaxed social setting. Also assume the two-handed handshaker and you work for the same company (he’s not a client or customer).