This is a mellow groove following a VI-IV-V-VI pattern, on the repeat the last chord is substituted for a II. In A, the Aeolian scale is effectively 'the white notes' making this really simple and effective to jam to.
If you're just getting going with your improvising try moving up and down the white notes by step (rather than jumping about), and think of the idea of 'questions' and 'replies' in your musical phrases.
I See Fire (from The Hobbit: The Desolation of Smaug)
(Piano/Vocal/Guitar). Composed by Ed Sheeran. For Guitar; Keyboard; Piano; Voice. This edition: Piano/Vocal/Guitar. Piano/Vocal/Chords; Sheet; Solo. Original Sheet Music Edition. Movie. 12 pages. Published by Alfred Music (AP.41025).