When someone says that the market is very bullish, they are stating that we are in a bull market. This generally means that prices are going up and "charging" forward like a bull. Investors are throwing more and more money into the market. By doing so, the market goes up and investments generally look really good. This is a great time to already have your investments in place because you can simply watch your money go up, seemingly with any investment. Even the bad investments can still see small upward mobility in a bull market.
On the flip side of the coin, a bear market generally refers to a decreasing market value. Much like a bear in hibernation, a bear market means the market is in decline. Usually, this is brought about by some sort of event such as the market collapse of 2008 in the housing market. This can set off a panic with investors and one by one, everyone pulls their money out of their investments and stock prices tumbled off the way side. It's a sad sight to see. If you've ever heard someone say that we are heading for or are in a recession, they generally refer to a bear market that has been going on for too long.
Lastly, a sideways market is one that basically does nothing. Much like purgatory, our investments get stuck in a sort of limbo. Prices may go up a little but then fall back to where they were. Or they may fall a little but then come right back up to where they once stabilized at. In this type of market, everybody goes home drunk and depressed because nobody is making any money. No one can make much off of a short (another type of making money but it rides on a loss happening) and nobody can ride a good bull market up to a higher price point. It's depressing really.