There are some scenarios in your league that may come up where teams agree to a trade shortly before games are scheduled to be played.
Once accepted, the trade enters a review period, which is determined in your league settings.
Once a trade processes:
Any player who has yet to play for that week is available to the new team immediately
Any player who has already played that week is locked into the original team's roster, along with any points. The team acquiring him will not be able to use him or any earned points until the following week. They will appear as "Off Roster" in the original owner's team, like Jimmy Graham in the graphic below:
With those two points in mind, it is possible for one owner to use both players involved in a trade in one week, while the other owner can't use any.
It's important to keep this in mind when accepting and offering trades. It may be best to wait a day or two to accept the trade. If needed, the commissioner has the ability to process a trade immediately instead of waiting for the full review time.