We usually understand the case of mamzer – a person who is forbidden to marry within the normative Jewish community – as a child born as the result of an adulterous or incestuous relationship. The Mishna on our daf introduces us to the position of Rabbi Akiva – a position that is not accepted as the halakha – which claims that the offspring of any forbidden relationship will create mamzerim. Thus, in a situation where a husband and wife divorced and the woman remarried, and then (after a second divorce or if her second husband died) they remarried, Rabbi Akiva believes that any children from that union would be mamzerim, since mahzir gerushato (bringing back his divorced wife) is forbidden (see 24:1-4).
From the next Mishna (49a) we learn that Rabbi Akiva’s position would include all cases of relatives who are forbidden to marry and the Gemara explains that the source for this ruling is based on his interpretation of the passages in Sefer (23:1-3) that place the law of mamzer in the same context as a forbidden sexual union. According to this, even Rabbi Akiva will rule only that a child from a forbidden relationship between relatives (issur erva) will become a mamzer. In response to the question that our Mishna has Rabbi Akiva ruling that even a case of mahzir gerushato will lead to mamzerut – and marrying one’s own divorced wife does not seem to be a case of issur erva – the Rashba argues that since they were once married their relationship is considered like that of family members. The Rambam reads the Mishna on 49a as offering two possibilities – either relatives who are forbidden to marry or any other forbidden relationship. This interpretation of the Mishna appears to be supported by the Talmud Yerushalmi.
It should be noted that we follow the position of Shimon HaTimni who rules that only a sexual relationship that would lead to a punishment of karet will lead to offspring who will be mamzerim.