Full Idea
We each of us not only have Dasein (our kind of Being), but we can lay claim to it. Also the Dasein of a thing 'is an issue for it' - we care about the kinds of creatures we can make ourselves into.
Gist of Idea
'Dasein' is Being which is laid claim to, and which matters to its owner
Source
report of Martin Heidegger (Being and Time [1927], p.67) by David E. Cooper - Heidegger Ch.3
Book Reference
Cooper,David E.: 'Heidegger' [Claridge 1996], p.29
A Reaction
Heidegger says other more puzzling things about Dasein. The second half of the idea is what makes Heidegger an existentialist, and an inspiration for Sartre.