We all think that this canine behaviour is so cute as this is our normal behaviour when our dogs do it. It looks so endearing and immediately engages our attention.
But it is important to consider that what are dogs are actually trying to communicate to us when they do this simple but cute gesture
Canine communication should always be interpreted in the context in which it is offered. Very often a dog will raise it's paw as his favourite person approaches . This is in anticipation of their arrival and dependent on the breed as active hounds often rush around the visitor until his excitement and energy die down and then he will want to be stroked. However, in this context the motivation of your dog is to get your attention, and hopefully a cuddle or a stroke! He will have 'smiling face', soft eyes and will offer you a face that you easily interpret as a kind and 'love me' one!
However, sometimes it can be a indication that your dog is unsure of something ahead on his walk. Perhaps he is considering whether he should move forward or not and is looking at his options.
It may also be a learned behaviour because you have smiled back at him whilst he raised his paw and he has connected the two together! Clever dog and if it works and he enjoys extra cuddles he may repeat the paw lift many times in the future.
Also , teaching a 'paw' or a beg' you may find that your dog uses a 'paw lift' to get something he wants because that is what has previously 'paid' for him . If you find that this is happening stop teaching these two commands and teach a good 'sit' or down' in a similar manner to which you taught the 'paw' . it is a very nice way for you dog to learn 'please' rather than perhaps 'pawing' at you which can sometimes can hurt you or a child or an elderly relative. Teaching and rewarding an alternative behaviour behaviour like a 'sit' works very well as a 'please' cue for most dogs which impresses friends and family too!.