A Gear Slot is a term used to refer to an unoccupied "space" in Max's inventory when he goes out on Break-Ins. Max has 5 Gear Slots that can be filled with 5 different items, selected in the Gear Selection Menu before the Break-In begins.
Each item, except the Pistol, takes up 1 Gear Slot. Some sets of items (like a set of Grenades from a single type, or a set of 10 Bugs) is considered a single item for this purpose, and will take up 1 slot. The Pistol takes up no slot.
Once 5 Gear Slots have been filled, Max cannot add more items to his carried gear. To add an additional item or set, Max needs to first empty a Gear Slot by de-selecting one of the carried items.
You do not have to fill all 5 Gear Slots in order to start a mission. In fact, you can begin a mission without selecting any Gear, which means you will start the mission with only a Pistol.
Note that once the Combat Mini-Game begins, these limitations are removed: It is possible to acquire Grenades from enemy bodies, obeying only the limit of up to 8 grenades of each type. This is the only type of equipment that can be collected during combat.