Epoch vault staking refers to the process of holding cryptocurrency in a "vault" (i.e., a digital smart-contract) for a certain period of time, known as an epoch, in order to earn rewards. This is known as "staking" because the user is essentially putting their funds "at stake" in order to earn a reward.
It will lock your tokens for the length of an Epoch, the first of which will be 60 days. The first 5 day period of each Epoch is the deposit/withdraw window. During those 5 days you are able to add and remove tokens from both the previous Epoch and the newly begun one. No rewards are accrued during this time. After 5 days, any tokens in Bonded Staking are locked for the remainder of the Epoch and they will accrue rewards which can either be withdrawn during the first 5 days of the following Epoch, or left to automatically compound and roll over into subsequent Epochs.
Each user will only be able to stake up to a maximum number of tokens, and total number of tokens staked will also be capped. These numbers are subject to change on an Epoch to Epoch basis.