In "Ode on a Grecian Urn," the speaker addresses the urn itself and the images on it. First, the speaker addresses the bride on the urn. She is frozen in time. She has yet to be ravished, so she is still "unravish'd." Critics have also suggested that "still" refers to her being a still (unmoving) image on the urn.
In the next, line the speaker addresses the urn, calling it a "foster-child of silence and slow time." The artist who made the urn is long gone because the urn is ancient. So, it is as if the artist is the parent and the urn (the work of art) is his child. Since the parent is gone, the child (urn) has become an orphan and has been adopted by time.
The urn is all visual. There are no words on the urn and, of course, no sounds emanating from it. It is therefore "silent." The urn is the foster-child of "slow time" because, having lasted so long with its images relatively unfazed, it is as if time has slowed down for the urn, making it seem more young/new than it actually is.
The speaker contemplates the silence and stillness of the urn and tries to derive its story (the urn is a "Sylvan historian"). The speaker considers that the frozen, silent images have a kind of immortality and incorruptibility:
Heard melodies are sweet, but those unheard
Are sweeter; therefore, ye soft pipes, play on;
Not to the sensual ear, but, more endear'd,
Pipe to the spirit ditties of no tone:
The speaker sees the images of characters playing melodies but can not hear them. Thus, the foster-child (urn) is forever silent. And since the images (and imagined melodies) on the urn are frozen in time, we might consider "slow time" as time that has slowed to the point of stopping. If time has slowed to the point of stopping, we can not hear the melodies nor see the characters move.
To Keats, the speaker, the images on the urn are frozen but they symbolize life. He tries to consider the urn like we might consider a photograph or pressing pause in our actual lives.