The Torah portion is Nasso, Numbers 4:21-7:89. In synagogues using the Triennial system, 5781 is year 2 and the Torah reading is Numbers 5:11-6:27.
This is the longest single parshah in the Torah. It continues the census, identifying the duties of different branches of the Kohanim, sons of Aaron. It discusses the procedure for when a husband is jealous. Many interpret this as poisoning a woman whose husband is jealous without proof, but I always thought this was simply a harmless procedure that disproved the husband's suspicions. It also discusses the procedure for the nazirite, a person temporarily consecrated like a priest, introduces the priestly blessing, and details the offerings from each tribe for the dedication of the Altar.The haftarah is Judges 13:2-13:25. This begins the story of Sampson, a nazirite from conception, an unusual thing (nazirite is usually a temporary status). This connects to the Torah portion, which discussed the rules for a nazirite.