Cross class abilities are simply abilities you can use from other Disciple of War / Disciple of Magic classes you train up.
You can see what skills are useable between classes by hovering over them when in the Actions window.
Some examples include Archer Level 4 Ability "Raging Strikes", or Pugilist Level 12 Ability "Internal Release", you level the respective classes to level started, than you can set the skills via the Additional window.
Other than the first two slots which you start with, and the slot you gain at level 10. You gain another additional skill slot every 5 levels, for a total of 10 at Level 50.
Each slot can be used to assign a cross class skill from the different classes you level up.
For jobs (Paladin, Warrior etc.), because you get more skills from doing Job Quests (5 in total), at level 50 you lose out on 5 Additional Skills (aka Cross class skills)
The limitations your talking about asides from having limited skill slots as a Job, is that when you are playing a class (Gladiator, Marauder etc) you can use cross-class skills from every other classes belong to Disciple of Wars / Magic.
But when you equip the soul crystal to become a Job, you can only pull from certain classes. For example, when you change to a Paladin, you only have access to Marauder and Conjurer cross class skills.
Hope this helps.
Edited, Sep 23rd 2013 3:31am by Suijin
Thanks for the quick reply! I have two more questions now:
1) So if I understand correctly, my lvl16 GLD would have access to 4 cross class abilities?
2) There's no limit on what level abilities my GLD can use? In other words, it's not like the sub-job system in FFXI where you could only use abilities up to half of your primary job? For example, could my 16GLD use an ability that was lvl12 in a different class?
Thanks again! :)