The main difference involves depth perception, the ability to sense how far in front of you an object is. This is not possible with a single eye, and is possible with two (or more) eyes.
The retina is essentially a 2D light sensor. It records the position that light arrives at in the back of the eye; coupled with the fact that this light is focused to a point* by the lens, and comes in through the "pinhole"** that is the pupil, this means that the retina can distinguish the direction (i.e. the angle) that light is coming from. It does not, however, have any way to determine how long light had to travel before entering the eye. In other words, in a uniformly-lit, featureless environment, a square with a 1-cm side length positioned 10 cm from the eye and an otherwise-identical square with a 1-meter side length positioned 10 meters from the eye will look the same. This is because the range of directions that light can enter the pupil after leaving each square is the same, which means they strike exactly the same area on the retina. Formally, we say that the objects have the same angular size $\theta$, defined as:
$$\theta=\frac{s}{r}$$
where $s$ is the distance from one end of the image of the object to the other end***, and $r$ is the distance to the object***. Two objects of the same composition and shape, different sizes, but the same angular size, will make exactly the same image on the retina. This means that a single eye does not have enough information to determine either the physical size or the distance to an object. At least one of these pieces of information is needed to determine the other one.
If you had only one eye, you could still have some way of determining distance: parallax. If the observer changes their position in some direction, due to the same formula above, the angular position of closer objects (with smaller $r$) will change more than the angular position of further objects (with larger $r$). So the object will cast different images on the retina before and after the observer moves. Based on how much the image of the object moved, you can distinguish close-up and faraway objects of the same angular size.
Obviously, strafing left and right whenever you need to determine the distance to an object is not exactly practical or energy-efficient, which is why animals that need to determine the distance to things quite often$^\dagger$ have two eyes, separated by some horizontal distance, facing in the same direction. The two eyes receive two slightly different images of each object, and by comparing the two images, the brain can estimate the distance to that object.
*Well, not quite a point. In reality, no lens is perfect, and people who need glasses suffer from a lens which doesn't properly focus light to a point on the retina, making the images on the retina blurry under certain conditions. Nearsighted people have a focal point in front of the retina, while farsighted people have a focal point behind the retina. Hypothetically, this does give one-eyed people with defective lenses some way of measuring the distance to an object, based on how blurry it is, but the price for this (namely, not being able to see properly at certain distances) is steep.
**Not quite a pinhole, but small enough to approximate one well, while large enough to let enough light in to form an image on the retina.
***For a flat object facing directly toward you, $s$ is the length of the object and $r$ is the distance to it. For non-flat objects, or objects oriented at an angle to the observer, this is more complicated, but you can still generally think of $s$ as some measure of the physical size of an object and $r$ as something like the distance to it.
$^\dagger$This usually means predators, who need to, for example, be able to jump the correct distance when ambushing prey. You'll notice that the eyes of prey animals, like rabbits, are not usually front-facing; rather, they're oriented to the sides. The advantage of this configuration is that they can see motion almost anywhere around them, at all times. The disadvantage is that the area where the vision of both eyes overlap (which is the only area in which they have depth perception) is much smaller than in a creature with two front-facing eyes. Presumably this is successful when coupled with the behavioral strategy of running away from any motion that looks suspicious, regardless of how distant it might be.
