A convalidation is needed when one or two baptized Catholics enter a marriage which is invalid and the couple now wishes to make the marriage valid. Indeed, convalidation is a new act of consent, which constitutes the beginning of the marriage in the eyes of the Church; it is not merely a blessing.
Typically, the marriage was invalid due to lack of form, which means that a Catholic did not observe the canonical form of marriage (consent exchanged before an authorized priest/deacon and two witnesses) and did not receive a dispensation to do so. In other words, the couple was married in a non-Catholic ceremony (e.g., before a justice of the peace, minister, rabbi, etc.) without an exemption from the Catholic Church.
Keep in mind that the canonical form of marriage is required only when the marriage involves at least one Catholic party. If your marriage was formed between two non-Catholics and, consequently, was celebrated outside of a Catholic ceremony, you do not need to seek convalidation, even when one or both parties are entering the Church. The marriage is considered valid since the form was appropriate to your status at that time.