Bull and Bear thematic funds are used to make directional bets on specific investing themes. The 2X and 3X versions mean they use various derivatives to increase the magnitude of the change in the correct direction.
Suppose that we had a Bull Spot Oil Fund and a Bear Spot Oil Fund. The Bull Spot Oil Fund would buy contracts such that when the spot (current) price of oil went up 1%, the price of a share of the fund went up 1%. The Bear fund would buy or sell contracts such that when the spot price of oil went down 1%, the share price of the fund would go up 1%.
The leveraged versions would potentially use options, futures and other sorts of contracts to get the behavior that the Bull fund went up the multiple of the change in the spot price and the bear fund went up the multiple that the spot price declined.
These sorts of funds involve some complicated sorts of trades and tend to have high expense ratios. They also tend to have what is called tracking error in that while the fund moves up or down the right amount daily, over time it does not move as much as it should for the aggregate movement of the theme it is tracking.