wide here means completely, wide awake means completely awake.
完全清醒的;完全醒着的

例句：

He’s wide awake and running around his bedroom. 他完全醒了，正在卧室里乱跑呢。

It was 3 a.m. and we were still wide awake. 当时是凌晨3点，我们仍然睡不着。