A telescope mount is the base of the telescope. It supports the telescope off the ground and allows it to point in different directions and at different angles.
The mount is arguably just as important as the telescope itself if you want to get a clear, sharp image. A cheap tripod will wobble at the slightest touch and any image in the telescope will be shaky. A heftier mount will keep the telescope still so that the image is clear, but this can mean that your telescope is much less portable. It’s about finding the right balance for your needs and budget.
Steer clear of flimsy, high street tripods in favour of better quality mounts from dedicated telescope brands and you should be alright.
You may see the terms alt-az and equatorial bandied about when looking at mounts. These refer to how the telescope can be adjusted to point at a particular part of the sky. Alt-az (short for altitude-azimuth) is the simplest system. The telescope can swing left-right and up-down on the mount, just like a camera tripod. An equatorial mount works in a similar way, but it’s tilted so that the telescope naturally traces along the paths of stars in the sky. This makes it possible to easily follow stars and other deep-sky objects over time.
Many amateur astronomers are partial to the good value and sturdiness of a Dobsonian mount. This is an alt-az mount that supports larger telescopes. Its design is so simple that it can even be made at home.