IPA: //ˌwɑːʃəˈtɪəriə//
KK: /ˌwɑːʃəˈtɪəriə/
A place where people can wash and dry their clothes using machines that they pay to use.
I went to the washeteria to wash my clothes because my washing machine is broken.
Washeteria is formed from 'wash' (from Old English 'wascan', meaning to cleanse or wash) and '-teria' (a suffix derived from Greek 'terion', meaning a place for). The word refers to a place designated for washing clothes.
Think of a place where you go to 'cleanse' ('wash') your clothes, which is what a washeteria is.