Each capital ship has four abilities. At each level, you may choose to either learn a new ability, or improve an existing ability. This means a freshly built capital ship gets one and only one ability to work with, so you need to choose carefully. Every time it levels up, you may choose to upgrade an existing ability or select a new ability, making your capital ship more powerful and more versatile as it levels up.
Capital ships have one "ultimate" ability that cannot be selected until they are level 6. This ability cannot be upgraded, and is effectively your capstone ability. Furthermore, capital ships must meet a minimum level to upgrade their existing abilities. You must reach level 3 to upgrade an ability once, and you must reach level 5 to upgrade an ability for the second time. Each ability can only be upgraded twice (so it takes three points to max out; once to learn it, plus two upgrades).
What this means is that you can make a capital ship that specializes in two abilities, or a capital ship that has three abilities but they're somewhat weaker. Usually it's better to specialize your capital ship to get more performance out of two abilities rather than trying to manage the antimatter requirements of three.
