To "pack" a packet of cigarettes is to whack them against a surface before opening the packet.
This is said to compress the tobacco.
Example: WikiHow describes the process
Many times while smoking a cigarette, the cherry will fall out because the tobacco is too loose or the cigarette is flicked too hard. To ensure that everything is packed tightly, you can "pack" a pack of cigarettes.
Does this process improve the integrity or longevity of cigarettes?