Battlecruiser - A large warship with longer range and greater speed & maneuverability than a Battleship, but less heavily-armored. BCs aren't meant to perform missions alone, but act as the core of larger forces.
Battleship - Large warships, with the biggest guns and heavy armor. BBs are often able to carry out missions alone, or with little support.
Carrier - Larger ships designed to carry multiple smaller ones into battle. They are usually much slower than their fighter craft, but have a much greater range, thus allowing for power-projection. They are lightly armed and armored, if at all, and rely upon their fighters for defense.
Corvette - Fast, Small to Medium-sized ships with the firepower of a Frigate, but with less range/endurance.
Cruiser - Fast medium-sized warships smaller than Battleships, and with less armor & firepower. CGs often carry more of a missile complement. Larger and usually better armed than destroyers, but with the same range and speed. Cruisers come in Light, Medium, and Heavy varieties, the latter two usually having heavier armor. Used against merchant vessels, pirates, blocade runners, etc.
Destroyer - A small, fast, heavily-armed warship. DDs are the smallest of the true "line" ships, often used for scouting, or as outer pickets for larger groups of ships. They are generally smaller, faster, and have greater endurance than Frigates.
Destroyer-Escort - DEs are Destroyers used mainly to guard other ships. Assigned to patrol and convoy duties.
Fighter - Small, usually fast, one or two-man warships with few weapons, and usually good armor, but poor endurance. Often based on a planet (and thus streamlined), or on a station or other ship.
Frigate - Fast, medium-sized warship. FFs are often relegated to patrol ("showing the flag") and possibly escort duties.