Life is possible on Earth because Earth has the particular characteristics and substances that are required by all known life forms. There are a few that are generally agreed upon. One of the main requirements is a liquid where molecules can react. On Earth, this is water.

Water can dissolve a wide variety of substances which enables the interactions of myriad chemical species that interact to carry out the processes required by life forms. However, other liquids are also (hypothetical) possibilities, such as ammonia or various hydrocarbons like ethane and propane. Another requirement is an energy source. Most energy for Earth comes from our sun. However, plenty of life exists in caves and deep ocean vents without energy from the sun ( see also here ). There are also some chemicals which seem to be the basis for all organisms: carbon, hydrogen, nitrogen, oxygen, and sulfur (and sort of phosphorus, but an exception has been found). These combine to form the proteins and nucleic acids which make up the genetic code of living things and are present on Earth in sufficient quantities and availability. These elements are quite common elsewhere in the universe too though, so don't expect this to limit life. There are a few other features of Earth which make it suitable for life, such as being far enough from dangerous galactic neighbors (e.g. stars emitting frequent gamma rays, large stars that might go supernova); Earth's inner core is molten metal, which generates a magnetic field to protect life from events like solar flares and solar wind; and also a moon that is large enough to stabilize the planet which then stabilizes the climate and prevents dramatic, dangerous variations.

There are a plethora of hypothetical biochemistries which may eventually prove suitable to sustain life. These hypothetical forms of biochemistry and the characteristics in the first paragraph are based on life that is known to exist though. As pointed out on ScienceLine here, biologists define life by meeting certain basic criteria. None of them are "needs water" or "based on carbon" though. With this in mind, some thing could meet the biological definition of life and not need any of what is listed in the previous sections. As given at the beginning, life is possible on Earth because Earth happens to have the stuff that known life needs. But keep in mind that unknown life could be very different.

The origin of life is one of the great unsolved questions in science. We know life is possible on Earth, because we see it all around us. We don't know if life is possible on other planets.

Here's one way to think about life starting on earth:
The origin of life is an example of ‘the whole is greater than the sum of its parts.’ Think of hydrogen + oxygen = water [H₂O], which is so incredibly different from hydrogen gas and oxygen gas. Think of a functioning car vs the parts that go into it but don’t do anything useful by themselves. Life is a very complex example of a whole [life] that is greater than the sum of its parts.

Here are links to work I've done about the origin of life:

This is a question under active research. We have some theories for how life started, and what we know is that life required water and some basic building blocks made of atoms of carbon, nitrogen, oxygen, and so on. However, from a scientifically philosophical point of view, we do not really know why life is possible on Earth. Part of the reason is that we simply do not have a lot of data about life. In other words, we only know some things about life on Earth, under very few sets of chemical and biological conditions, but we don't know about life in other places in the universe or even in our solar system. This is part of the reason that we are seeking ways to study ice, water, and biological molecules on planets, moons, and asteroids in our own system - to understand what makes the Earth so suitable for life, and to get some answers for the questions, "Are there other conditions under which life is possible? If so, what are these conditions and what does living organisms look like under these conditions?"

It’s pretty crazy that life is possible on Earth. There are many factors, and they all work together perfectly so that you and I can live comfortably on Earth’s surface. There are 6 main reasons:

1) We are just the right distance from the sun. Any farther away (like Saturn or Jupiter) and our water would all be frozen. If we were any closer (like Mercury), our water would all evaporate!
2) Speaking of our sun, it’s just the perfect size. Really big stars tend to burn really hot and don’t live very long, and smaller stars are usually unstable and blast their planets with bursts of deadly radiation.
3) Earth is also special because it is surrounded by a giant magnetic field that protects us from solar flares.
4) We are also surrounded by this amazing thing called the ozone layer that is really high in the sky. Without it, we wouldn’t be protected by all the dangerous and deadly radiation in space.
5) Our moon is also important. Earth is actually tilted and spins at an angle, so it wobbles a little bit. However, our moon stabilizes this wobble and keeps our climate and weather stable!
6) Finally, our solar system is nestled nicely between the major arms of our galaxy (the Milky Way). Our solar system is far enough away from other ones so that they don’t tug and pull on ours and that keeps us safe from collapsing. It’s pretty amazing that all of these factors work together to create a world we can live in.

Life as we know it is possible on Earth because Earth exists within the range of conditions that life can inhabit. In general, this means that Earth has liquid water, as well as sources of energy, either through geologic activity or through sunlight, for living things to use this energy to grow and reproduce. It is possible that there are other forms of life in the universe that we have not yet discovered and that could not exist on Earth, however. Similarly, if these other forms of life exist, then Earth-like life probably could not exist where these other life-forms do.