There are multiple victory conditions in Advance Wars By Web, not all of them are possible every game.
Kill Everything that's not yours and you win, simple
Head Quarters Capture Edit
Capturing a HQ defeats the owning player, no matter what, if a player owns multiple HQs the capture of any of them eliminates the owner.
Lab Monopoly Edit
If there are no HQs Labs take their place, they work like HQs except you have to capture all of a players labs to eliminate them.
In some games taking a set number of properties under your control wins you the game. Most of the time this option is left off, but be sure to check for it when joining a game!
Sometimes the only way to win is to get the other player to give up
Not actually a victory condition, but if both players agree be clicking (set draw) the game is officially tied, use it to end stalemates.