Joining a particular parish, to me as EO, means saying that that's the place you'll participate in the sacraments, such as Communion, and Confession. It also means stewardship-- you are going to support that parish's life with your gifts, talents (such as teaching Sunday school, or choir, or parish council) and also financially. It is a commitment to having a personal relationship with the people in the community and the priest (unless the parish is extremely large, when you can't know everyone).
The priest at your parish can vouch for you and sign a paper saying you are an EO if you are called on to be a witness at a wedding (like best man/maid of honor) or a godparent, if you are doing that in another parish where they don't know you, which are serious responsibilities.
HTH