He likes to travel and sail in his boat, and speaks with a French accent.
In A Special Trip to Grandpere's House, when referring to grandpere at 25 seconds, Dad Tiger mentions "oh dad, you've outdone yourself". Later at 8 minutes, there is a paw print which belonged to Dad Tiger "from when I was a little tiger like you" and Grandpere comments "seems like just yesterday your dad was a little tiger like you".
The word grandpere means grandfather in French and is a way for French children to say "grandpa" in which Grandpere Tiger is Daniel's grandpa.
There was a character Mister Rogers' Neighborhood named Henri Frederique de Tigre. His son's daughter Collette Tiger also referred to him as "grandpere". A witch predicted Collette would marry Daniel Striped Tiger.
If Grandpere is the father of Dad Tiger and not Mom Tiger and if Mom Tiger is Collette, then this would probably indicate that Collette told her son what she used to call her grandfather and that Daniel chose to use the term to refer to his paternal grandfather and not his maternal grandfather (assuming they're different people) for reasons unknown.