he waved his hands about a lot when he was excited

about在这里是副词， wave his hands about 相当于说“双手乱舞”，a lot 相当于程度副词，类似于very much等表达

所以He waved his hands about a lot when he was excited.意思相当于他一兴奋起来就双手使劲挥舞

他兴奋的时候使劲挥手。

你把句子截错了。应该是
he waved his hands about
a lot
when he was excited

他激动的时候会经常挥他的手。

使劲