Bipedalism simply means to walk on two limbs rather then the more common four limbs. It is a popular misconception that humans are the only animals that do this. Certainly bipeds are a lot rarer than quadrupeds (those that use four limbs for movement). But there are still plenty of examples in nature of animals who walk on two legs.
Humans being able to walk on two legs rather then four means that we are around six feet from the ground rather then three or four feet as with other primates. This gives us a chance to better see any approaching predators. It also means that we use up less energy when walking as only two sets of muscles are being used rather then four.
As well as this we have the advantage of being able to navigate places where many quadrupedal animals couldn't. For example we can climb fairly well compared to a lot of big predators capable of eating us, and are pretty adaptable in where we can go. for example a human being chased by a lion could swim to relative safety by entering some deep water.
Having two limbs spare has also allowed bipedal and semi-bipedal animals to use things such as tools. Humans and other primates will use complex tools to help them to find food and to affect their surroundings. This is one of the many things what puts humans above all other animals in terms of intelligence.
The disadvantage of this is that in humans we are a lot slower then most other animals. In humans case however our increased intelligence makes up for this. While we might not be able to outrun a predator we can either outwit them or will be intelligent enough to find somewhere that they cant get to us. Bipedal balance also isn't as good as quadrupedal balance, as we are higher up, and aren't as balances with our weight distribution.
Chimpanzees are probably the most famous biped other then humans. Their use of two limbs for walking rather then four has allowed them to develop dexterity and tool use with their other two limbs. They have been known to scare away leopards that attempt to hunt them by pelting them with sticks and stones while in the trees. They can do this because of having developed the opposable thumb, which comes from being a biped rather then a quadruped.
Birds as another example all primarily use two legs for walking. And the flightless birds such as Ostriches can certainly be considered as bipedal as humans are. Being on two feet rather then on four allows most birds to have a better starting position for taking off when flying as well. They can also see further as they are standing upright and aren't as low to the ground.
Kangaroos are another example for a successful biped. They have evolved on two legs to be able to become very good at jumping and moving fast. They now have no natural predators and are one of the most successful species in Australia. Although there is a case for calling them a triped, as their tail acts as a third balancing limb most of the time.
This means that they can see whether its safe to take off or land. And that they don't have to use up as much energy when taking off as they would if they were on all fours. If they were on four limbs they might in fact require a run to get them into the air, rather than being able to take off more or less vertically. Also hovering in the air to feed, as well as landing on vertical surfaces would be a lot harder with four limbs.