In some special realms such as Juratania/Eastern Lands you may come across monsters with the tag “Your spawn” under their name/level information. This indicates that this particular monster was spawned by your character and not another player, it is a great way to see quickly if a monster is yours or not.
Anyone can attack a monster spawned by another player and get credit for it themselves rather than the player that spawned it however in some cases in particular in the Dragons of the East pack the difficulty of the monster is based on the spawning character so you may find that unless it says Your spawn the monster may be too hard for you or for that matter too easy.
The Your spawn addition is meant as a visual guide and nothing more or less than that.