A political organization is a non-profit organization that is specifically designed to bring in and spend money related to public office. This public office can be local, state, federal, and so forth — what matters is that it is a public position. The political organization is able to campaign for, fundraise for, and otherwise support candidates within a public office, but is not allowed to operate on a for profit basis.
Political organizations need to follow a number of strict standards, but for the purposes of the IRS, they are an exempt organization. They will still need to file their tax returns, but they are able to claim exempt status at that time. They will not need to pay taxes, and will need an EIN for the organization, and organizational documents on a legal level. Their EIN will also be necessary if they want to open separate bank accounts, establish credit lines, and hire employees to continue their work, all of which they can do and still remain under exempt status