I think he means personal prayer while the Liturgy is going on. Correct me if I'm wrong.
I can't correct you on what Ai had in mind, I'll wait for him/her.
I think I understand what you mean by "personal prayer while the Liturgy is going on", but something about this formulation doesn't sit well with me. Obviously, it is more proper to come to the church on time and participate attentively in the liturgical services by listening carefully to what needs to be listened to, praying what needs to be prayed, singing what needs to be sung, bowing, crossing oneself, etc. than it is to show up whenever and, paying no heed to the service, "doing your own thing".
At the same time, attentive participation in the liturgical services will naturally bring certain of our needs to mind. The litanies will remind us of people and needs to pray for, certain hymns or prayers will remind us of these things, maybe even the saint(s) of the day. If one takes that opportunity to pray a little more fervently for those people and those needs, I don't think that's necessarily the "careless" type of personal prayer, but rather that's the liturgy doing what it's supposed to do: feeding our personal prayer and spiritual life within the Church and enabling us to exercise the priestly ministry that is proper to all the baptised. There are even some prayers during some services which presuppose we are offering our own prayers privately along with the liturgical prayer that is going on publicly. To a certain extent, I would say that closing oneself off to this in order to focus on the rites or the words is also a form of "not participating".
Another issue is that phrase itself: "personal prayer". We mean something rather limited when we use it, but there is a sense in which all prayer, individual or communal, is "personal", because it is carried out by persons and is itself the manifestation of that relationship we have with God by which we are persons.