Activeness is the state or quality of being active. The opposite is passiveness.
In sexual contexts, "active" can refer to a role in gay anal sex of the parter who penetrates, while the "passive" partner is the one who is being penetrated. In BDSM contexts, "active" can refer to a top, while "passive" can refer to a bottom. In consensual adult spanking, the "active" partner is the spanker, while the "passive" partner is the spankee.
An active artist, author, actor, producer etc. is one who is still alive and working creatively in their hobby or profession. An active website is one who is still online and being maintained by its webmaster.