The physical meaning of inductance
When we use the term 'inductance', we're usually shortening what should actually be called 'self-inductance'.  

When a current flows through a wire, a magnetic field is produced around that wire, with its field strength in proportion to the current strength, changing as the current changes.  

We also know that a changing magnetic field will induce a voltage over a wire in proportion to the strength of the field and the rate at which it changes.  

So, if we have a wire with a changing current flowing through it (think AC or DC with some ripple), then it will produce a changing magnetic field around itself. This changing magnetic field will then induce a voltage back across that same wire, but this induced voltage will be of the opposite polarity to the voltage of the original applied current.  

Since the induced voltage opposes the applied voltage/current, the apparent effect is an increased impedance (complex resistance, or resistance with a phase angle), and since the strength of the induced voltage increases in proportion with the frequency of the applied voltage/current (as frequency is the rate of change), the inductor's impedance increases with frequency.  

The inductance (with the unit Henrys) of an inductor is a measure of this self-inductance effect.  

(Self)inductance is increased by coiling the wire around so that the coils all contribute to and share the same magnetic field.
Wrapping the coils around a magnetically permeable core also increases (self)inductance by 'concentrating' the magnetic field.