Sovereignty: Control level for a given solar system. Comes in levels 1-4 with levels 1-3 taking each a week to kick in and sov 4 being constellation sovereignty, which I won't try to explain for sake of the mental health of all of us. Sovereignty 3 is needed for Cynojammers and Jump Bridges (which, in a nutshell, allow for faster travel by bypassing the stargate network and getting friendly capital ships into cynojammed systems).
ISK reserves: ISK = Ingame money (InterStellar Kredits), which coincidentially has the same abbreviation as the Icelandic currency (where CCP is based).
cyno-jammers: Capital ships cannot use the ordinary stargates, but have their own jumpdrives that need to calibrate to what military experts call a Cynosural Field. Cyno-Jammers prevent creating cyno fields, effectively making a system immune to surprise visits by hostile capital ships.
capfleet towers: Where's that mentioned?
director level access: The other comment sums it up well, sudo. ;o)