Backpacks almost act as a personality piece for adventurists. While other essential items are based on need, environment and activity, backpacks are used consistently throughout allowing you to pick and choose backpacks based on what you like. There of course are some restrictions around size weight and applicability for the given activity but for the most part, packs are fairly universal.
The immediate consideration for packs is their size. Size of packs is measured in liters and it applies to the internal volume of the pack along with any externally accessed zip pockets like the brain and rain cover pocket. These can range from 15-20-liter packs that have a similar volume to a school bookbag to massive 70+ liter packs designed for extended expeditions into the backcountry. To put this into perspective a 30-35-liter pack is commonly an appropriate size for any day long activity. This allows you to pack all necessary specialist gear, an extra layer water and food in a reasonable size. A 50+ liter pack is bringing you into overnight / multiday trips with space for tents and sleeping gear.
With different sized packs, you also encounter different weights. While not as common a point of pack selection as the other properties of the pack, for those with ultralight or weight reduction concerns, it may be a variable to consider. The larger the pack, the more they generally weigh. Frame size, material and padding can also add to the overall weight but are usually viewed as a tradeoff for a more comfortable carry especially in larger packs.
There are also options in the purpose and requirements of the packs. For example, climbing packs are slim in figure with little to no exterior straps and pockets to prevent the pack from snagging on rock or ice. They are also generally made of more rugged materials to avoid punctures or abrasions on the walls. In comparison, hiking packs generally have a lot more exterior functions and features like back air flow systems, load lifters and even water bottle side-pockets that can be deceptively useful. With these different features suggest the different activities the pack can be used for and its overall versatility can be assessed. For example, a basic day pack can be used for a variety of sports like hiking, cycling, Snow sports and even on some top rope climbs as you are not risking damage to the pack whilst having a reasonable size for these day-long activities.
Internal frame packs are probably the most common packs you will see today. It involves a hidden frame that shapes to the size and length of your torso for a better fit. The better fit helps in both performance and comfort allowing you to extend your abilities and carry heavier loads without the discomfort of the older external frame models.
External frame packs are the older more traditionalist outdoorsman packs. The frame itself allows for increased versatility over the newer internal frames with your ability to attach additional items / storage systems to the outside of the pack. Even so, the frames themselves are less comfortable and have decreased efficiency in terms of weight balance and management.
Day packs are smaller carry systems without the addition of a dedicated frame. These systems are designed specific for day activities without the space or functionality for overnight / multi day use. Their benefit over the larger packs boil down to weight, price and breathability.
Don't worry too much about going out and buying a state of the art ultralight backpack. For most day activities, a school bag will work just as well, although significantly less functional and versatile. If you are thinking about buying a pack, to begin, consider a internal frame 40 or 50 Liter pack size. This will be big enough for 1-2 day trips and overnight camping whilst not being too large to bring on day trips in a pinch. Its also a good size to get comfortable thinking about and packing what you need and trimming the fat of luxury or unnecessary additional items that you may get away with packing in larger carry systems.