What does 起来 mean in this phrase?
This 起来 serves as the resultative complement of 收.

It is required because you cannot say “把被子收_吧”. You must specify in what state you want to put the 被子 via the action 收. e.g. 把被子收进屋子里, 把被子收到柜子里, etc.

You can say “把被子收走” or “把被子收了”, too. The choices of complements make slight difference.

For some reason, when 起 is not followed by an object, you must put 来 or other verbs or prepositions after it. e.g. it's possible to say 收起被子, but you have to say 把被子收起来. (Some speakers may accept 把被子收起, but it sounds a little stilted and incomplete to me. Another similar particle is 回, which is often accompanied by 去. But 把被子收回 still sounds acceptable to me.)

I think the closest definition out of the four is:


  1. used after a verb indicating beginning and continuation of an action or a state


This 起来 in 收起来 indicates that, after the completion of the action 收, the blanket is in a temporary state such as protection or preservation. It may sound redundant, but is required by the Chinese grammar.

起 can be consider as “to happen/to arise”, which by itself has almost no meaning. But if you look at many similar collocations like 收起, 亮起, 挂起, 升起, 隆起, 突起, etc. It might be related to another meaning, too:


  2. indicating an upward movement


Also, don't confuse 把被子收起来 with 收起被子来. The latter means he starts to put the blanket away, which is extremely unlikely to be used in daily conversations. 收起(了)被子 can express the same meaning in many contexts without 来. I don not know what exactly is the function of 来. But this does not have much to do with your question.