Lamentations 3:49, "My eye pours down and doesn’t cease, without any intermission," is a powerful expression of inconsolable grief and ceaseless weeping. Let's break down the meaning:

"My eye pours down...": This uses vivid imagery to describe tears flowing uncontrollably. The word "pours" suggests a heavy, continuous stream of tears, like a flood.
"...and doesn’t cease...": This emphasizes the persistence of the weeping. It's not a fleeting moment of sadness, but an ongoing, unrelenting state of grief.
"...without any intermission...": This is the key to understanding the verse's depth. "Intermission" means a break or pause. So, there is no relief, no respite, no stopping point to the tears. The grief is constant and unbroken.

Overall Meaning:

The verse illustrates a profound, overwhelming sadness that is constant and inescapable. The speaker is consumed by sorrow, unable to find any comfort or relief. It signifies:

Unending Grief: The speaker experiences pain that seems to have no end in sight.
Helplessness: The speaker is unable to control or stop the tears, suggesting a feeling of being overwhelmed by the situation.
Deep Trauma: The imagery suggests the speaker has experienced something deeply traumatic, leading to this constant state of mourning.

Context within Lamentations:

Lamentations is a book of mourning poems that lament the destruction of Jerusalem and the suffering of its people. The speaker (often interpreted as a personification of Jerusalem or the remnant of Judah) is expressing the deep sorrow and devastation caused by the Babylonian conquest. This verse specifically highlights the continuous and unrelenting nature of the suffering, underscoring the depth of the tragedy.

In essence, the verse captures the utter despair and unending sorrow of a person (or a nation) who has experienced unimaginable loss and suffering.