In physics in general (not just in quantum physics), the term "superposition" just means "linear combination". Any vector quantity can be thought of as the superposition of basis vectors. For example, if we travel $\sqrt 2$ miles north-east, this can be thought of as the superposition of travelling $1$ mile north and $1$ mile east. A scalar quantity can be though of as a superposition too - for example, the complex number $1+i$ can be thought of as the superposition of $1$ and $i$ (whether or not this is a useful point of view depends on the context).
The unexpected thing in quantum physics is that the state of a system behaves like a vector quantity. In classical physics a system is either in a given state or it is not - a switch is either on or off; a particle is either at this location or it is somewhere else. But in quantum physics the state of a system is a linear combination of basis states (and, to add a further twist, the multipliers of the basis states are complex numbers rather than real numbers).
So whereas a classical switch can only be off $|0\rangle$ or on $|1\rangle$, a quantum switch (also known as a qubit in quantum computing) has a state
$\alpha |0\rangle + \beta |1 \rangle$
where $\alpha$ and $\beta$ are complex numbers (and, conventionally, they are scaled so that $|\alpha|^2 + |\beta|^2=1$). This combination of classical states is a superposition.
