Memory Towers are great, impenetrable objects scattered throughout the Labyrinth. They are used by Malfeans to conceal information from the Hive Mind by concealing it from themselves. If nothing in the Hive Mind knows a thing, that fact is absent from the entire Hive Mind's awareness, so the Malfean can keep something secure.
The interiors of the Towers are inaccessible by the Hive Mind, so any Spectre within one will not be able to communicate its knowledge to the outside. They are supported by struts of black crystal. This crystal is the "substance" of Harrowings, which no longer happens to spooks since the Sixth Great Maelstrom. Touching it puts the spook into a Harrowing, which is intended for Specters to lose their Spite and become Orphan-Grinders. This ensures that any information they may obtain about the Memory Tower doesn't spread through the Hive Mind.
Many Memory Towers contain plots, plans, and the like, while others contain Relics that the Malfean feels is too dangerous or too useful to allow others to possess or even to know that it exists. Grandmother has a Memory Tower concealing God's Arrow. The exact nature of God's Arrow isn't known to the Malfeans, but they do recognize that she does not want anyone getting anywhere near to it.