Tai Sui (太歲, "Grand Duke") is the symbolic deity of the year — the Earthly Branch ruling the current year. Disturbing the Tai Sui direction is considered inauspicious, and people whose zodiac animal conflicts with the year are said to "offend Tai Sui" and require remedies.
Short answer
Tai Sui (太歲, "Grand Duke") is the symbolic deity of the year — the Earthly Branch ruling the current year. Disturbing the Tai Sui direction is considered inauspicious, and people whose zodiac animal conflicts with the year are said to "offend Tai Sui" and require remedies.
In depth
Each year is assigned an Earthly Branch (one of 12, cycling through Rat, Ox, Tiger, Rabbit, Dragon, Snake, Horse, Goat, Monkey, Rooster, Dog, Pig). The current year's Tai Sui sits in the corresponding compass direction — for example, in a Tiger year, Tai Sui sits in the East-North-East direction (60°–75°).
In Feng Shui, you should avoid: facing the Tai Sui direction during major undertakings, sitting with your back to it, or doing renovation/construction in that sector of your home. Doing so is said to invite obstacles, illness, and financial loss.
In Ba Zi, your Year Branch determines whether you "offend Tai Sui" in any given year. The four scenarios are: Ben Ming (your year matches the current Tai Sui), Chong (your year clashes 180°), Hai (your year harms by 30°), and Xing (your year punishes). Remedies traditionally include carrying Tai Sui amulets and avoiding major life decisions during the conflict year.