The common sense answer is that in your mind you create a model of the world around you based on input from your senses. The external world is the set of things that your senses are detecting. Clearly the model you create in your mind is not an accurate or complete model of what exists outside. It is a selective and subjective model, no doubt geared to the needs of our more primitive ancestors, for whom the ability to perceive the world was a matter of survival in a Darwinian sense. It is also possible for your mental model to be subject to hallucinations or imaginary effects, which render it even less like the 'real' outside world.
If you wish to establish with more certainty the extent to which your mental model is a realistic one (ie that it maps to attributes of external reality in a way that is consistent) then there are two obvious categories of test you might employ. One is to compare your model with those created by other minds- do other people appear to perceive the world in a way that is compatible with your perception of it? If so, then you might be inclined to conclude that your model is not a purely personal figment of your imagination. The other is to create instruments which can detect and quantify the properties of the constituents of the external world. If I place a fragment of a potato chip in a computerised chromatograph, I can get a print telling me its chemical composition- something I cannot do with my senses alone.
Now consider your mental model, which you consider 'real'. I would say that in some sense it is anything but real. When you look at a tomato and see that it is red, the colour red is entirely a product of your mind. There is no red in the external world- there is only light of a certain set of frequencies which your brain interprets as red. When you smell a rose, the idea of a smell is purely imaginary- what exists in the outside world is certain molecules in the air which interact chemically with specialist cells in your nose. When you feel cold, that sensation is a mental interpretation of messages from your nerves which are triggered by effects that ultimately boil down to the interaction of infrared radiation and the molecules of surrounding material (air, clothing etc) with the molecules of your skin.
So, there is an external world- it is what is continued to be experienced by other people when you are asleep- and what is in your mind is an interpretation of it, one shaped by evolution and largely shared by other minds.