The customer can serve herself, and then pay for the goods with the minimum of delay.
In the sentence, the customer can be a male or female. But the pronoun 'herself' has been used. I'm confused with the use of 'herself'. Please explain it to me.
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We don't have widely-adopted gender neutral singular pronouns. The authors are trying to avoid using himself to describe both genders, and so use herself. This is quite a common practice. Other possibilities might be to say himself or herself, or customers can serve themselves.
See this reference for plenty of detail
The gender-neutral pronoun is they / them (nominative / accusative), but things get a little confused with the reflexive form because not everyone is entirely happy with themself (they want to stick with themselves even in contexts where the referent is obviously singular).
In short, unless he wants to rely on the (somewhat outdated) principle that he / himself can validly be used with no specific implication of gender, OP can "correctly" use either of themself / themselves.
But it's always going to be a bit awkward, and some people might object to the specific choice (or even simply object to "singular they" on principle). So many people would simply rephrase so they don't need to make any such choice (Self-service allows the customer to pay for the goods with the minimum of delay, for example).