a charge: a duty or responsibility entrusted to someone to keep faithfully
This is the most common use of the word, and it comes straight from the verb behind it, which means to keep, watch over, or guard. A charge is something handed to you to look after: an assignment you are responsible for and answerable for. The phrase that runs through the law is to keep the charge of the LORD, or the charge of the tabernacle, meaning to carry out the service God has assigned and to make sure it is not neglected.
Most often the charge belongs to the priests and Levites. Their charge was the upkeep, protection, and right handling of the sanctuary and its worship, a sacred trust that could not be left undone or done carelessly. Because the duty was real and ongoing, the word easily widens to cover any solemn obligation a person is bound to keep, as when God says Abraham kept my charge along with my commandments.
When the priestly service was organized into rotating shifts, the same word came to name a division or course of men assigned to a turn of duty. The idea is unchanged: a charge is still a charge, now spread across teams who take it in turns.