A ridge is an easy line to agree on
Borders need something both sides can recognize on the ground. A mountain range offers exactly that: a high crest that separates the drainage on one side from the drainage on the other. In the medieval frontier between Moldavia and Transylvania, the boundary initially followed the watershed of the major rivers in the area, meaning the line was set along the high ground that divided where water flowed [1]. The same logic appears in the Jizera Mountains, where old maps show borders drawn through the mountain terrain and treated as a recognizable feature of the landscape [3].
The practical appeal is that a watershed is self-describing. You do not need a surveyor to invent a straight line through forest; the land itself tells you where the divide runs. That makes mountain crests attractive to people who must agree on where one jurisdiction ends and the next begins.
Mountains are hard to cross, which makes them useful as frontiers
A mountain frontier is difficult to monitor except at the main passes, and that quality shaped how medieval borders worked in practice [1]. The terrain itself did much of the separating: movement between the two sides concentrated at a few gaps, while the high ground between them was rugged and lightly watched. A border that follows a mountain range therefore gets some of its dividing function for free from the landscape.
This does not mean mountains cause borders. It means that where a range already exists, rulers and communities have a strong reason to treat it as the seam between their territories. The Moldavian-Transylvanian case shows the line being managed as a mountain frontier, with the old traditions of mountain frontier management in the Kingdom of Hungary influencing the western borders of Moldavia [1].
The line can move when the land becomes valuable
A mountain border is not fixed forever by geography. In the Eastern Carpathians, more intensive economic exploitation between the 16th and 17th centuries produced the first documented conflicts between Moldavian rulers and the inhabitants of Bistrița, and the Saxon representatives argued for fixing the common boundary along the course of the disputed rivers instead [1]. In other words, when resources in the mountains became worth fighting over, the principle for drawing the line was contested: watershed versus river course.
That detail matters for the general question. Mountains sit on borders partly because they were convenient, but the exact line along a mountain can be redrawn as economic interests change. The mountain stays; the border on it can shift.
Some border mountains are not just scenery
Not every border mountain is a quiet ridge. Borderland volcanoes in Latin America sit on international boundaries while also being the subject of geological monitoring, so the mountain is simultaneously a political line and an active geological system [5]. That combination makes the border a place where science and politics meet, because monitoring a volcano means paying attention to a feature that is also a national boundary.
The broader point is that mountains on borders are not one kind of thing. Some are old, eroded divides used for centuries as watershed frontiers [1]; some are mapped and toured as border landscapes [3]; some are living geological hazards on the line between countries [5]. The common thread is that a mountain gives people a durable feature to hang a border on, even when the reasons for that border, and the dangers around it, keep changing.
Sources used in this answer
The border of Moldova with Transylvania and the specifics of medieval mountain borders
The medieval border between Moldavia and Transylvania initially followed the watershed of major rivers, and later economic exploitation of the Eastern Carpathians sparked conflicts over whether the boundary should instead follow disputed river courses.
Multispecies households in the Saian Mountains: ecology at the Russia-Mongolia border
The paper examines human-animal relations and landscape use in the Saian Mountains along the Russia-Mongolia border through ethnographic case studies.
Borders on the old maps of Jizera Mountain
Old maps of the Jizera Mountains show how borders between Czechoslovakia and Germany were depicted and perceived in a mountainous region.
Through the unexplored mountains of the Assam-Burma border
The paper describes mountainous country along the Assam-Burma border in the context of local villages and groups.
When the vertical becomes horizontal: experiencing exploding mountains in borderlands
Borderland volcanoes in Latin America sit on international boundaries and are entangled with the politics of geological monitoring.