Geographically, much of the Western Highlands of Scotland are closer to Ireland than to the Lowlands. As transportation by boat was much easier than travel overland, Northern Ireland would have been comparatively accessible to the West Highlands, and vice versa. While we now see the countries "Northern Ireland" and "Scotland" no such national entities existed until relatively recent times.
Scottish clans in Ireland.
For centuries they were both divided into clan and tribal holdings. Frequently a clan would have property and clanspeople in both. One such example is a branch of Clan Donald known as "Clan Donald of Dunnyveg and the Glens". "Dunnyveg" refers to a castle in the Hebrides while "the Glens" is in Northern Ireland. The lineage of clans in Scotland and and tribes in Ireland show common ancestors. For instance, O'Neill, MacNeil, MacLachlan, MacSweeney and Lamont all descend from King Aodh, King of Ailech (a medieval kingdom in present-day Donegal), c. 1030.
Celts, Norse, Anglo-Saxons and Normans.
In addition to the primarily Celtic populations of Ireland and the Scottish Highlands, there were incursions and migrations from the Norse, England and Lowland Scotland. The English and Lowland Scots were a mix of Anglo-Saxon, Norse, Celts and Normans. England repeatedly invaded Ireland. These incursions produced little lasting effect until the "Plantation" of Ulster in the 17th century. Read more about the Ulster Scots on our Scots-Irish page.