The vision at Ostia is described in Augustine's Confessions, Book IX, Chapter 10. 'She', of course, is Monica:
As the day now approached on which she was to depart this life--a day which thou knewest, but which we did not--it happened (though I believe it was by thy secret ways arranged) that she and I stood alone, leaning in a certain window from which the garden of the house we occupied at Ostia could be seen. Here in this place, removed from the crowd, we were resting ourselves for the voyage after the fatigues of a long journey.
We were conversing alone very pleasantly and "forgetting those things which are past, and reaching forward toward those things which are future." We were in the present--and in the presence of Truth (which thou art)--discussing together what is the nature of the eternal life of the saints: which eye has not seen, nor ear heard, neither has entered into the heart of man. We opened wide the mouth of our heart, thirsting for those supernal streams of thy fountain, "the fountain of life" which is with thee, that we might be sprinkled with its waters according to our capacity and might in some measure weigh the truth of so profound a mystery.
And when our conversation had brought us to the point where the very highest of physical sense and the most intense illumination of physical light seemed, in comparison with the sweetness of that life to come, not worthy of comparison, nor even of mention, we lifted ourselves with a more ardent love toward the Selfsame [Idipsum], and we gradually passed through all the levels of bodily objects, and even through the heaven itself, where the sun and moon and stars shine on the earth. Indeed, we soared higher yet by an inner musing, speaking and marveling at thy works.
And we came at last to our own minds and went beyond them, that we might climb as high as that region of unfailing plenty where thou feedest Israel forever with the food of truth, where life is that Wisdom by whom all things are made, both which have been and which are to be. Wisdom is not made, but is as she has been and forever shall be; for "to have been" and "to be hereafter" do not apply to her, but only "to be," because she is eternal and "to have been" and "to be hereafter" are not eternal.
And while we were thus speaking and straining after her, we just barely touched her with the whole effort of our hearts. Then with a sigh, leaving the first fruits of the Spirit bound to that ecstasy, we returned to the sounds of our own tongue, where the spoken word had both beginning and end. But what is like to thy Word, our Lord, who remaineth in himself without becoming old, and "makes all things new"?
There are some interesting features to this religious experience. One of the more interesting is that Augustine claims it was a shared experience that arose out of conversation. Augustine and Monica are having an intense and lively conversation about the life of the saints in heaven, looking out at the garden at Ostia. The conversation becomes extraordinarily absorbing as they talk about higher and higher things, reaching up to God, and then, says Augustine, "we just barely touched her [i.e., divine Wisdom] with the whole effort of our hearts". In the conversation, as Augustine relates, both in the very act of conversation had a deeper sense of themselves and, through this, just a bare intimation, a touch or glimpse, of the conversation of heaven itself. Conversation itself becomes a prayer, and conversation as prayer gives a momentum intelligentiae, one moment of understanding, of the heavenly life. The conversation that is itself a prayer is the first taste of heaven.
It's become popular recently to talk about Augustine's background Neoplatonism, but it is difficult to imagine most Neoplatonists, and certainly any pagan Neoplatonists, having an experience like this, despite the emphasis on meditative and inward 'ascents' that most Neoplatonists have. Thomas Williams has an interesting paper on this subject, called "Augustine vs. Plotinus" (PDF). I think some of his claims are a bit strong, but the basic point, I think, is right: this is a thoroughly Christian experience. And it is noteworthy that Augustine talks of it in Trinitarian terms.
And, as Williams notes, one of the marks of this experience is its contrast with the earlier religious experiences at Milan. The 'ascents' at Milan, which more closely conform to Neoplatonist models, occur, as this one does, just prior to a death: the death of Adeodatus, Augustine's beloved son. The experienced provide no comfort. The whole of that scene of Augustine's life ends in greater misery and unhappiness. But this does not happen here; Monica dies just as Adeodatus does, and she is not an unimportant part of Augustine's life. It cannot have been easy, and Augustine is frank about the pain of the parting. But there is no misery, and through the pain there is joy. The religious experiences at Milan were, effectively, experiences for Augustine alone; but in the vision at Ostia, he experiences a tie that goes beyond death. He experiences the conversation of the saints, and because of that, death no longer quite has its sting.
Another interesting thing about it is the name used of God here, Idipsum, or Selfsame. It sounds like something a Neoplatonist would say, doesn't it? But the name comes from the Psalms. Much of Book IX is influenced by Psalm 4; chapter 4 of Book IX is an exegesis of the Psalm.
In pace in idipsum dormiam, et requiescam; quoniam tu, Domine, singulariter in spe constituisti me.
(This is the Vulgate; I'd have to dig up the actual Latin Augustine uses, but it's very similar.) As Augustine says in Chapter 4:
And with a loud cry from my heart, I called out in the following verse, "Oh, in peace!" and "the self-same [Idipsum]!" Oh, what said he, "I will lay me down and sleep!" For who shall hinder us, when "shall be brought to pass the saying that is written, Death is swallowed up in victory?" And You are in the highest degree "the self-same," who changest not; and in You is the rest which forgets all labour, for there is no other beside You, nor ought we to seek after those many other things which are not what You are; but Thou, Lord, only makest me to dwell in hope.
When Augustine speaks of God as Idipsum, the Selfsame, it is no doubt his Neoplatonist background that leads him to pick up on it as a name of God; but his usage is not Neoplatonist, but follows the usage of the Latin Psalms. In the vision at Ostia, Monica and Augustine have actual experience of that of which the Psalmist speaks, the Idipsum or Selfsame, the sure ground of hope. And Monica learns this lesson well; after the experience, leaning at that window over the garden at Ostia, she turned to her son and said, "What am I doing here any longer?" And so she, as the Psalm says, soon falls asleep in peace, in the Selfsame, in whom is her hope.
