I'll try to hit upon the major arc plot points. There are many individual eps that were pretty cool but had no bearing on the overall season arc. See
here to get some recaps of the eps like Twilight, Northstar, Similtude & Chosen Realm.
Last season had Enterprise entering the Delphic Expanse to find a race called the Xindi who were duped into destroying Earth (more on this later). The resolution of the attack on Earth that ended season 2 lasted for the entirety of season 3. The Temporal Cold War still had an impact as folks from the future were screwing with the Xindi because they needed someone to destroy the Federation before it got started.
I should quickly note that the Xindi are comprised of 5 different races: Primates, Reptilians (the most aggressive), Sloths, Aquatics and Insectoids. They don't always get along and have to pass all important decisions through a council comprised of the 5 races.
First off, the Expanse is an area surrounded by this cloud that messes with navigation. The Expanse itself was explored by the Vulcans and none of them returned. The only trace was a transmission that looked like it was taken directly from Event Horizon. The Vulcans went bonkers. So they warned Starfleet not to go into the Expanse and would give no aid. T'pol resigned her Vulcan commission and took a field commission aboard Enterprise to help out.
Upon entering the Expanse after shaking some Klingon headhunters they found these huge spheres that were surrounded by cloaking fields. Additionally, the ship had to deal with spatial distortions that would destroy parts of the ship, injure crewmembers and do other bad things. These distortions were pretty random. The crew found a way to insulate the ship using a material called trellium-D. Problem is that the material is poisonus to Vulcans and drives them nutty. As the season continues we learn that T'pol has become (by her own experimention) permanently altered by her contact with the trellium so that she will never be able to fully suppress her emotions again.
So, the Xindi are building this Uberweapon to destroy Earth. Along the way, Archer learns (while compromising some of his morals) that the race who build the Spheres are the ones manpulating the Xindi. Turns out that the Xindi will join the Federation in the future and Humanity are the ones who save the Xindi from the Spherebuilders. The Spherebuilders are slowly changing the Expanse into space that they can inhabit. Hence all the spatial distruptions.
Archer ends up gaining the trust and respect of a few influencial Xindi along the way and tries to use their political power to stop the attack on Earth. It ends up not working as the Reptilians launch the attack. Good prevails in the end, Archer and crew are shot back to 1940's Earth where time traveling aliens have teamed up with the Nazis to conquer Earth. Yay.
Again, there is a ton more to it than just that but it's the overall story of Season 3. Some interesting infighting, a romance between Trip & T'pol, Archer doing whatever it takes to accomplish his mission and other things were pretty neat. Not the best season of Trek ever, not even close to the last 4 seasons of DS9 but it got better as it went along. The final 6 eps were very solid and included some very cool space battles.
