The underlying idea
A crystal system describes the symmetry of the repeating unit that builds the structure — the relative lengths of its three axes and the angles between them.
It is a statement about internal structure. A specimen can be a shapeless lump and still belong unambiguously to the cubic system.
The seven
Cubic has three equal axes at right angles: fluorite, halite, galena, diamond. Pyrite, despite its cubic habit, is tetragonal. Tetragonal has two equal axes and one different, all at right angles. Orthorhombic has three unequal axes at right angles, as in topaz.
Hexagonal and trigonal are built on a three-fold or six-fold axis; quartz, calcite and corundum are trigonal. Monoclinic has one oblique angle, as in gypsum and malachite. Triclinic has no right angles at all and is the least symmetric of the seven.
System is not habit
Habit is the shape a crystal actually grew into; system is the symmetry it must obey. Pyrite grows as cubes, as octahedra and as twelve-sided pyritohedra, and all three are cubic.
Beginners routinely identify from habit and are routinely wrong. Habit is a hint. System is a constraint.