There would seem to be two parts to the answer.  The first involves the nature of life, the second the history of life.

As in all scientific explanations, it is important to remember our limits.  In this case, the key event, the origin of life, occurred some billions of years ago. 

Equally important, all organisms appear to have descended from a "last universal common ancestor", known as LUCA, and so represent only one possible type of life. 

It is possible that life in other parts of the universe might be different.

The living systems that we know about have certain common properties.  Most importantly, they import energy to maintain and reproduce their structure. 

This requires that they establish of region of the universe that is highly structured and organized  - these are properties that are associated with "low entropy". 

Since living systems obey the laws of thermodynamics, generating a local region of low entropy requires that the total amount of entropy in the universe as a whole increases. 

If we are going to spend energy to maintain a low entropy region (and this does require energy), then it makes sense that we will want to separate this region in a stable way from the outside world. 

One way is to build a border - in the case of cells, this border is constructed of lipids and is known as the plasma membrane.

However, a membrane built only of lipids poses a barrier to the movement of energy rich molecules into the cell, and waste products out. 

In all organisms known, these "transport" functions are carried out by membrane proteins.  These are molecular machines that use energy to move specific molecules into and out of the cell. 

All living organisms have plasma membranes built using the same basic components, lipids to generate the basic barrier and proteins to control movement of materials across the barrier. 

Within the membrane, there is concentrated solution of proteins and other molecules and molecular complexes known as the cytoplasm – it contains a number of distinct structures, such as ribosomes.   Within the cytoplasm is the genetic material, composed of DNA.

In prokaryotic organisms (bacteria and archaea) the genetic material is embedded in the cytoplasm, in eukaryotic organisms (like us humans), the genetic material is located within a distinct compartment, the nucleus, connected to the cytoplasm by nuclear pores.  

Remarkably enough, bacterial, archaeal and human (eukaryotic) cells all have the same basic type of cytoplasmic structure. 

If we think of the definition of a cell, it really comes down to a plasma membrane enclosed cytoplasm and also contain genetic material.  

One of the great breakthroughs in biology was the Cell Theory of Life, which was established in the mid-1800s. 

Based on many (many) observations and experiments, it became clear that living organisms do not arise spontaneously in the modern world. 

All organisms examined to date (ranging from potatoes to koala bears to fruit flies, petunias, sequoias, worms and whales) are composed of cells or the products of cells and cells arise only from other cells. 

Evolutionary theory applies to populations of reproducing entities, such as cells and organisms (composed of cells).

In evolutionary theory, the presence of structurally related components in diverse organisms is due to one of two mechanisms, either the structure was inherited from a common ancestor, or it was "invented" independently, a process known as convergent evolution (the wings of insects, birds and bats are examples of convergent evolution).

The fact that all organisms examined (so far) are composed of cells, and that these cells have very similar structures, suggests that organisms "inherited" their cells, and that the last universal common ancestor of life was composed of one or more cells. 

The harder question remains, how did the original cell form, how did life originate? - there are currently a number of competing ideas (hypotheses) - check out this example.