Inspiral refers to the path of binary stars which are losing energy and approaching each other. Several things can cause the loss of energy including tidal force

Tidal force

The tidal force is a secondary effect of the force of gravity and is responsible for the tides. It arises because the gravitational force per unit mass exerted on one body by a second body is not constant across its diameter, the side nearest to the second being more attracted by it than the side...

s, mass transfer

Roche lobe

The Roche lobe is the region of space around a star in a binary system within which orbiting material is gravitationally bound to that star. If the star expands past its Roche lobe, then the material can escape the gravitational pull of the star. If the star is in a binary system then the material...

, and gravitational radiation. The stars describe the path of a spiral

Spiral

In mathematics, a spiral is a curve which emanates from a central point, getting progressively farther away as it revolves around the point.-Spiral or helix:...

 as they approach each other. This sometimes results in a merger of the two stars or the creation of a black hole

Black hole

A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...

. The last several revolutions of the stars around each other takes only a few seconds in the latter case.