People often think “Private Mass” means Mass where the priest and God are alone and no one comes in.  Right now the circumstance dictates that no one may attend, but that is not the norm.  Typically, at least one person is to be in attendance to offer the responses.  That is Church Law.  However, the priest may say Mass without a server for a just cause…an event where there is not a server or as in our case right now where such is not even possible.
This is because the priest stands both “in persona Christi”, in the person of Christ AND “in persona ecclesiae”, in the person of the Church.  So, he is not saying Mass “talking to himself”…he is addressing God and responding on behalf of the Church in a legitimate absence of the people.
 
So Mass is NEVER private in the sense that it is just the priest and God…the Church is always present.  Then why is it called “Private Mass”?  In Latin the phrase is “Missa Privata” which is erroneously translated as Private Mass.  And from that error comes the erroneous understanding of a so-called Private Mass.  The Latin verb “privo, privare, privatus, privata, privatum” means to deprive, to have something taken away, to lack something.  A Missa Privata is not a Mass that is private, but a Mass that is deprived or lacking.  
 
It is a Mass lacking all the requisite ministers, a choir and sung responses, and all external solemnity such as incense and processions, etc.  It needs to be noted that no Mass lacks power, effect, or spiritual perfections, but it can lack elements that contribute and fulfill its external solemnity.  Typically, a private Mass is merely an unannounced Mass as on a priest’s day off or during vacation.  Normally, anyone can attend at any time.  In some monasteries where there is one Conventual or communal Mass with one priest celebrant, each monk will offer his private Mass at a side Altar in the morning before attending the communal sung Mass.  
 
Since the liturgical reform of the last century, concelebration (where several priests vest and participate in offering Mass at the same time) has become common.  But, every priest has the right to offer Mass privately when he does not have the obligation of being the principal celebrant.  The exception to this is for the Sacred Triduum where private Masses may not be offered.  This year and for this year only, Pope Francis has made an exception.