The cellphone allows people to show strangers that they belong, that they are part of a community somewhere.
show 可以接双宾语,其中直接宾语可以是 that 宾语从句,间接宾语是strangers。本句第二个 that 宾语从句,中间不用and 连接,是解释前一个 that 从句的内容。
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二个that都是从属连词,引导宾语从句,作不定式to show的直接宾语。二个that从句是并列关系,二项并列用逗号连接,暗示列举不完整,有未尽之意。
belong在此意为:are accepted and liked by the other people in a group.