The easiest way for me to describe STO is to say it's
Guild Wars with a Star Trek skin over it.
You create a character from two and a half factions - the Federation, a full faction; Klingon Defense Force (KDF), a full faction; or the new Romulan Republic (after a certain level, flows into Fed or KDF). Then, you pick a 'class' - classes consist of tactical (DPS), science (Heals/Buffs/DPS), and Engineering (Buffs/Debuffs/Tank). The skills you can use depend on the class you pick. Finally, you pick a ship - there are three classes of ships: escorts (DPS; like Defiant), cruisers (tank; like Enterprise-D), and science vessels (heals/buffs; like Voyager).
Once all that's chosen, you can either play the story through or join a fleet (e.g. guild) and play with friends. Along the way, you gain NPCs who join your ships' crew - these are your away team and ship team. They go with you on missions and give your ship special abilities.
There is a mix of land and space-based combat, and most missions try to mix it up. Most of the races are in there, and there are certain 'arcs' that include enemies like species 8472 (called Undine in STO), RSE, Cardassians, Breen, and Vorta/Jem'Hadar.
My Admiral, for example, has completed the story. She is a science officer focusing on medical who flies around in a Prometheus-class starship (the actual on-screen Prometheus). That means she can use her healing while the ship focuses on DPS, which makes it a cool balance in battle.
It's hard to sum up in a post. Is it everything I would like a Star Trek MMO to be? Absolutely not. Does it get actual voice actors from the show to do things and try to keep everyone happy as much as possible? I think that's a definite yes. It's a nice ST-inspired game to play casually.