This is a complex question which requires more analysis than would be possible here, but the most obvious points can be summarized as follows:
---All three of these men made a deliberate effort to simplify the language of poetry and to bring it as close as possible to the way people actually talk, instead of using obvious 'poetical' phrasing as was the norm in much English verse until that time. This was the ideal Wordsworth wrote of in his 'Preface' to Lyrical Ballads. It is, however, only one aspect of the Romantic movement and there are other poets of their time, and later, who did not hold it as a goal to the same extent as these three. One can differentiate Burns from the other two, of course, because of his use of Scottish dialect, but this is a special manifestation of the desire for poetry to imitate genuine speech and not simply to conform to an elegant poetic ideal.
---Burns, Wordsworth and Coleridge were all imbued with the same spirit of change and egalitarianism that swept through Europe (and America) in the years before and immediately after the French Revolution. The generation of poets who followed them--Byron, Shelley, and Keats--were born too late to have experienced this and were all subject to some extent to the disillusionment that occurred when the Revolution gave way to the endless wars of the Napoleonic period. So there is a positive, optimistic quality in the first phase of Romanticism, perhaps expressed best in Burns's 'A Man's a Man for A' That' which was never re-captured by subsequent generations of poets (though in Burns this was tempered by realism in his even more famous poem 'To a Mouse').
--Perhaps most obvious of all is that there is an intensely personal quality in their verse which became the norm for succeeding generations of poets. It is not that such a tendency did not exist in poetry prior to the early Romantic period, but beginning with the age in question the emphasis upon personal emotion became greater, coupled with the other tendencies noted above.