What is a chimney liner installation?

If you have a wood burning stove you should have a metal tube (usually 6 inches or 8 inches that run from your stove up through the chimney to the roof. The round cross section is easy to clean with a wire brush and it keeps the high heat from damaging your existing chimney. Depending upon the stove you might use a double wall pipe or even triple wall if you are going to be near combustible material. For example you might use triple wall if the stove is in the basement and the flue must pass through a closet.
Newer stoves with reburners and/or catalytic converters burn hotter than the old, single baffle air tight stoves. The high heat means there is little creosote but it can damage brick and mortar chimneys if they are not protected.

Chimneys are made of bricks and mortar.
In older homes, over time, the mortar between bricks deteriorates and can allow noxious fumes to penetrate through into upper floors or even closer to the ceiling on the same floor, or perhaps the attic space.
To remedy that, a hollow tubing made of ceramic tiles or metal is stacked/inserted inside a chimney, (much like building w/ bricks/mortar)
This prevents fires, noxious gases from entering your home, and even further deterioration of your chimney.
Hope this helps.

As both @LuckyGuy and @Bagardbilla have stated, this is an tube inserted in the chimney. When I was in the chimney cleaning business many years ago, it was usually the ceramic type. At that time, most chimneys I dealt with were plain wood-burning fireplaces or stoves, not the higher-tech stoves or inserts with the reburners and cat converters. In addition to the heat transfer issues, the smooth surface of the liner makes cleaning more efficient by eliminating the nooks and crannies that can hide creosote.

Welcome to Fluther.

Here is a relatively simple isometric / cross-sectional drawing of a chimney. As you can see from the diagram, chimneys are not quite as simple as they appear to those who don’t understand them. They’re not just a collection of brick and mortar that the homeowner hopes is more or less plumb.

The interior surface of the chimney, the flue, is lined with a heat-resistant material (more heat-resistant than masonry brick, that is) which will stand up to the hot and often corrosive environment of the combustion gases, as well as to the regular brushing that may be required to maintain the flue for some fuels, notably wood. That, in essence, is the chimney liner.

In modern chimneys, the brick is primarily a structural material that will withstand some heat, and the liner is the material that provides the flue for the exhaust gases and protection for the interior of the chimney itself from those gases.