Sub- or Secondary Stats are values calculated using your Level, Base Stats and gear. They are also modified by effects from equipments, cards and skills. Some of them can be seen in your Status Window (Alt+Q) but most of these require the use of @info self to correctly determine.
There is a separate page for MATK here.
MATK is used for calculating damage dealt with magical attacks and the effectiveness of Heal as well. Its main sources are level, gear and INT.
There is a separate page for ATK here.
ATK is used to calculate damage dealt with auto-attacks as well as the damage dealt by physical attack skills. Its main sources are gear and STR (or DEX if using a bow, whip, gun or instrument).
ASPD is a stat governs the speed of all animations, most notably auto-attack. It also serves as the cooldown of many, if not most, physical attack skills. As such, ASPD is one of the most important stats for all physical damage classes. ASPD is increased by AGI and DEX, but it can be increased directly with a number of equipment and cards as well. ASPD is calculated relative to your level - this means that it is possible to have a high ASPD already in the lower levels, but you'll have to keep spending points in AGI in order to keep it that way.
The precise formula for ASPD is currently unknown, but an estimate can be calculated with: Base ASPD * ( 1 + (2 * AGI + DEX / (6 * Base Level)) )
Base ASPD is weapon-specific (140 for unarmed).
HIT is the stat that determines how often your physical attacks hit an opponent. This fact makes it likely the most important stat for physical damage classes. However, the necessity of HIT can be ignored with the use of a Phreeoni card. HIT is increased by Weapon Refines, Level and DEX. Landing a critical hit temporarily increases your HIT by 100 in addition to other effects.