30 And truly Jesus did many other signs in the presence of His disciples, which are not written in this book;
31 but these are written that you may believe that Jesus is the Christ, the Son of God, and that believing you may have life in His name.
These verses are John's purpose statement.
John indicates that he was selective in what he wrote. He only mentions six miracles specifically, although he states that there were others (John 2:23; 3:2; 4:45). He selected, with the guidance of the Spirit, the signs that prove Jesus is the Son of God.
The "many other signs" (v. 30) may be referring to post-resurrection signs done in the presence of just His disciples.
John was probably writing to those who already believed, encouraging them to continue in the faith. The verb tense of "believe" (v. 31) indicates an ongoing action.