Bouldering is a type of climbing which doesn't involve ropes, as such it can be seen to be more risky when compared to top roping. People often boulder harder than they climb because the moves are shorter (a 4m bouldering problem when compared with a 15m top rope will take less overall exertion), bouldering is very good for building strength, but not stamina.
Grades for bouldering are often in V or font grades, the higher the number though, the harder the climb in general. There are many grading systems and there is no standardised system however they mostly follow the hgiher is harder principle.
Bouldering is normally done above a mat, inside a large fixed padded mat is often used, outside a smaller foam mat is used, which is then carrier from one boulder to the next. Often people use multiple bouldering mats depending upon the direction and difficulty of the climb.
High-ball bouldering is basically soloing, it refers to climbs which are very high and shouldn't be fallen off, consequences of such bouldering can be very serious if things go wrong.