“snack-size/single-use portions” of something (typically something you’re saving for later use or giving to someone). For example, after you make a ton of some solution, like an antibiotic solution, and you need to freeze it for storage, you don’t want to have to freeze-thaw the whole 50mL or whatever any time you want 1mL of it. So, before you freeze it, you can “aliquot aliquots” (yup, it’s both a noun and a verb!) such as 1mL portions into eppendorf tubes before freezing. This way, you only thaw what you need! note: repeater pipets are a great help here!
The term is also often used when scientists give another scientist a little bit of something they made. So, for example, I might give my colleague an “aliquot” of a protein I’ve made – just enough for what they need it for.