"Empírica" means that the birth was attended by a "partera empírica", a midwife with expertise acquired through experience but without formal qualifications:

"Parteras empíricas: un apoyo al sector salud [...]
Una partera empírica es una persona sin estudios profesionales que se dedica a dar atención a las embarazadas durante el parto, así como los primeros cuidados después del mismo, aunque hay que diferenciarlos de las que sí tienen estudios o son enfermeras"
http://www.gaceta.udg.mx/Hemeroteca/paginas/178/9-178.pdf

It is not necessarily accurate to call these people "untrained", since, as the text just quoted goes on to say, "una tercera parte ha recibido adiestramiento por otras colegas y personal de instituciones o centros de salud, como el Instituto Mexicano del Seguro Social"

The correct term is traditional birth attendant or TBA:

"A traditional birth attendant (TBA), also known as a traditional midwife, community midwife or lay midwife, is a pregnancy and childbirth care provider. Traditional birth attendants provide the majority of primary maternity care in many developing countries, and may function within specific communities in developed countries.
Traditional midwives provide basic health care, support and advice during and after pregnancy and childbirth, based primarily on experience and knowledge acquired informally through the traditions and practices of the communities where they originated. They usually work in rural, remote and other medically underserved areas. TBAs do not receive formal education and training in health care provision, and there are no specific professional requisites such as certification or licensure. They often learn their trade through apprenticeship or are self-taught; in many communities one of the criteria for being accepted as a TBA by clients is experience as a mother."
http://en.wikipedia.org/wiki/Traditional_birth_attendant

See, for example, the following document:

"Table 17. Percent distribution of Women and Husbands, by Type of Assistance during Childbirth
Type of Assistance
Doctor
Obstetric specialist
Midwife puskesmas
Village midwife
Private midwife
Traditional birth attendant"
http://www.jhpiego.org/files/mnhSurveyRpt_Indo.pdf