Yes, the card you have been given has a larger memory than your current one.
Open your tower case,(remember to turn off your system at the socket, but keep the plug in the socket for earthing purposes). Remove the current card and replace it with the new one(there should be a small screw to remove). Give a firm press to seat the card on the motherboard, but be carefull not to put too much pressure on the card. One thing to note, DO NOT touch the gold coloured connection strip on the card.