Wrap is an attack which goes on for several turns.

The graphics in that game don't show any real animation, so that won't be of much help.

Example of the text in the game.

Ekans uses wrap.
Pikachu uses thunderbolt.
Pikachu is hurt by wrap.
Ekans uses tackle
Pikachu uses thunderbolt.
Pikachu is hurt by wrap.
Ekans uses tackle

In short. The pikachu pokemon is continuously hurt by the wrap placed by the enemy ekans. Eventhough the snake's body is wrapped around the helpless little mouse it seems to be able to do a tackle.
In this case the snake does the wrap, so if I have to see that in real life, I can hardly imagine it doing a tackle or something of the sort.
But the attack is hardly used in the game, so it won't be a problem to the poke-fans, I think.