One of the amazing things about Digimon is that the monsters can shift back and forth from different stages of maturity and strength. This process is simply called evolution. Let's have a look-see at Terriermon's evolved forms! There are plenty of story spoilers to go around, so proceed with caution.
Type: Lycanthrope (Beast Man) Digimon
Attacks: Dum Dum Upper, Gatling Arm
Note: His name is sometimes spelled "Gargomon" in Roman letters on merchandise. However, there is already a gargoyle-based Digimon named Gargomon, so I am going to assume that the correct spelling of Terriermon's Adult form is indeed "Galgomon."
Whenever Terriermon is faced with a strong opponent and needs that extra boost of power, he evolves into Galgomon. In the beginning, Jian didn't want Terriermon to ever evolve because once turned into Galgomon, he'd run amuck and be difficult to deal with. Terriermon was still a game character the first time he evolved into Galgomon. He went on a rampage and ended up hurting himself, so once Terriermon became real, Jian made sure to tell him time and time again not to evolve. Terriermon agreed, but once he was hit by an attack coming from Renamon, he sort of slipped and gave in to the evolution process. Although he did go ballistic for a little while as Galgomon, he eventually calmed down. Ever since then, Terriermon has been able to control himself as Galgomon, and Jian slowly but surely started agreeing to Terriermon's evolving.
With the powerful guns attached to his arms, Galgomon can fire at his opponents (Gatling Arm) AND punch them in the jaw from below (Dum Dum Upper). Cool.
Type: Cyborg Digimon
Attacks: Rapid Fire, Golden Triangle
Galgomon further evolves into Rapidmon! To reach this stage quickly, he needs the help of his best friend Jian, Jian's Digivice, and a special kind of card. Like his name suggests, Rapidmon is magnificently fast both in attacks and movement.
So here's some backstory. Terriermon (eventually Galgomon) was fighting bravely against the sheep Deva, Pajiramon, but not really standing a chance against her. Earlier on, Jian had mysteriously obtained a Blue Card, and he really didn't want to use it as he had no idea what could happen, but as he was running out of options, he eventually had to. The result? Rapidmon and the destruction of Pajiramon!
Rapid Fire is a super fast shooting attack. With Golden Triangle, Rapidmon forms a triangle with his body in order to send off a powerful beam.
Type: Machine Digimon
Attacks: Giant Missile, Burst Shot
In order to evolve into his most powerful form, Terriermon has to merge with his partner, which comes in handy since Jian is quite a skilled fighter. SaintGalgomon is slower than Rapidmon, but makes up for it in raw power. Being a machine Digimon, SaintGalgomon has weapons hidden all over his gigantic body. With Burst Shot, he fires off a frightening amount of little missile weapons, and with Giant Missile, he... shoots two giant missiles located in his shoulders. The missiles are very cute! They can go from looking angry to happy. SaintGalgomon almost looks like an oversized action figure.
So, story time! Rapidmon was getting so badly pummeled by one of the big boss Digimon that one of his cyborg parts disintegrated, and he eventually devolved back into Terriermon. Jian took the blame for everything, and Terriermon kindly reminded him that he's not alone in this. Determined to protect everyone and to make it back home safely, the two of them took the form of SaintGalgomon together for the first time.
Type: Lesser Digimon
Attacks: Never seen attacking
A stage below Terriermon, he only devolved into Gummymon once throughout the series, in the last episode, even. It was after the kids and their Digimon finally managed to defeat the final boss and bring peace to the worlds. It would be dangerous for the Digimon to continue living in the Real World because of the possibility of evolving out of control, so they all devolved into their Baby forms and were transported back to the Digital World. But fear not, one of the Digimon Tamers movies takes place a few months after this happens, and they're all back together with their Digimon pals then. Phew!