Hi, います(or いる) is the progressive form. For example: あそぶ(play)　⇒　あそんで＋います（playing） たべる（eat） ⇒ たべて＋います(eating） する（do） ⇒ して＋います(doing） When one changes a verb into the progressive form, it needs to conjugate it and add います/いる at the end. (The two answers above are just right, I think)

it comes from the verb "asobu" (to play) and it means 'playing'. the sentence means 'the children are playing'

hi, flora i will try to answer. "asondeimasu" it is mean you are doing something... (ongoing) if u are not put "imasu" it means many activities are ongoing...（more than one activity) ex.. 私は六時におきて、朝ご飯を食べています 6 o'clock i am waking up, breakfast. i hope it can help