Answer: The Gemara in (Pesachim 113b) teaches that one who doesn’t participate in a seudas mitzva is ostracized in Heaven. The Rashbam writes that an example of such a seudas mitzva is a bris seuda.
Following this, the Rema (YD 265:12) writes that somebody who avoids eating at a bris seuda is considered ostracized in Heaven. Thus, the Pischei Teshuva (YD 265:18) writes that one who makes a bris should be careful not to invite others explicitly to their seuda as they may not be able to attend.
The Aruch Hashulchan (YD 265:37) quotes the Midrash (Pirkei Derebbi Eliezer 29) which implies that a bris seuda is a mitzva mideoraisa, though writes that one doesn’t need to be concerned about this ostracization nowadays. One should still make every effort to attend.
R’ Moshe Feinstein (OC 2:95) writes that the minhag remains not to explicitly invite people to a bris seuda. He explains that there is a greater mitzva to attend a chasuna than a bris seuda. Thus, he allows one to shave during the sefira, if necessary, to attend a wedding, though not for a bris seuda. Nonetheless, the baby’s father has a mitzva to host a seuda for his son’s bris and it is inappropriate for those invited to turn down their invitations.
In conclusion, the minhag is for parents to inform people that they are making a bris seuda. This serves as a reminder as to the greatness of the simcha of this mitzva.