As you might expect in Puerto Rico, I think this is a straight translation of the expression "party admission". This, in US law of evidence, means "a type of statement that appears to be hearsay (an out of court statement) but is generally exempted (excluded) from the definition of hearsay because it was made by a party to the litigation adverse to the party introducing it into evidence."
https://en.wikipedia.org/wiki/Party_admission

The reference to Rule 803 (a) and (d) of PR's rules of evidence supports this. Rule 803 is about admissions, and it lists circumstances in which a prior statement is not a prueba de referencia, which means hearsay: Thomas L. West III gives "hearsay evidence" for "prueba por referencia" in his dictionary, and PR's Rule 801 (c) confirms this:

"Prueba de referencia: Es una declaración que no sea la que la persona declarante hace en el juicio o vista, que se ofrece en evidencia para probar la verdad de lo aseverado"

And here are the relevant parts of Rule 803:

"No empece a lo dispuesto en la Regla 801, no se considerará prueba de referencia una admisión si se ofrece contra una parte y es:
(a) una declaración que hace la propia parte, ya sea en su carácter personal o en su capacidad representativa;
[…]
(d) una declaración hecha por una persona agente o empleada de dicha parte, que esté relacionada con un asunto dentro del ámbito de la agencia o empleo y que haya sido hecha durante la vigencia de la relación.
http://www.ramajudicial.pr/sistema/supremo/Reglas-de-Evidenc...

So these are admisiones de parte, which are not regarded as hearsay evidence and are admissible: prty admissions. They are not necessarily statements by the defendant and are not necessarily admissions of guilt as such.

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Note added at 1 hr (2019-01-12 15:05:15 GMT)
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As Rule 803 shows, it refers to statements by the party, or a representative or employee of the party, against whom it is introduced in evidence, which corresponds to a party admission ("made by a party adverse to the party introducing it into evidence").