To Rush is to quickly install an Agenda in a remote server and score it. This is done by building a remote server with one, or ideally two, "end the run" ice while the runner is still building their rig.
Corporation decks designed to win by repeatedly doing this are known as Rush decks.
Rush is commonly mistaken for Fast Advance. Although some hybrid decks incorporate both rush and fast advance strategies, the two are not related to each other.
To rush an agenda, the corp must be able to move the game from early game to mid game as fast as possible. This usually means setting up a remote server with at least two pieces of ice of different subtypes. The reason two pieces are needed is because the runner may be able to install the icebreaker needed to get through one ice on their next turn or they may have an Inside Job that allows them to bypass the first piece of ice on the server. Rush ice are usually cheap, "end the run" ice across all three main ice types. Examples include Ice Wall for barriers and Quandary for code gates. Guard is an "end the run" sentry that has an added ability stating it cannot be bypassed which helps counter Inside Job. Chimera is also a popular "end the run" ice that allows the corp to choose its ice subtype when rezzing it.
In addition to setting up the remote, the corporation must have the credits available to rez the ice on the server and advance the agenda that will be installed in the server. With this in mind, rush decks often include cards that generate a lot of money with little time investment such as Restructure and Hostile Takeover.
Although rush decks are strong in the mid game, they struggle with early game, and late game. This means the runner should pressure R&D and HQ as much as possible at the start of the game prior to the corp setting up their remote server. Once the server has been set up, the runner must try to get the necessary pieces of their rig set up to get through the remote server effectively. Once the pieces are in place, the remote is generally easy to access and the corp will have trouble protecting their agendas for enough time to score. In addition to building their rig, there are certain cards that help get into a remote when needed. Inside Job, allows the runner to bypass the first ice. Parasite can trash the ice which usually has low strength.