An investment account is simply an account that allows you to buy investments like stocks, bonds and mutual funds. These accounts are available through various institutions, including online stock brokers, banks, mutual fund companies and full service stock brokers. Although each institution will have different fees and minimums for their accounts, they all function in the same way.
There are two major types of investment accounts: taxable and tax-advantaged. Taxable investment accounts are funded with after-tax money and receive no special tax treatment of any kind. They are completely flexible and the money in them can be used to purchase any investment that the holding institution offers. Tax-advantaged accounts include accounts like Roth and Traditional IRAs, 401Ks, 403bs, Coverdells and 529s. Each of these has specific income limits and withdrawal requirements, but the money inside them can generally be used to purchase any investment offered by the holding institution as well.
Some investment accounts have high account minimums (6 figures or more). These accounts are marketed for high net worth investors and may come with special perks, like free investment advice or free trades. However, they still function in the same basic way as accounts without such privileges.
When choosing an investment account, it is best to decide what investments you would like to buy before choosing a place to open your account. Although all brokerage firms have access to the entire stock market, they each offer a different selection of mutual funds. If you know you want to purchase the Vanguard Total Stock Market Index Fund, for instance, then Vanguard is the best place to open your account, because it's the best place to buy that fund. If you want to purchase a Vanguard fund and a Fidelity Fund, either choose an institution that sells both, or open an account at each Vanguard and Fidelity to get the best deal on both of your funds.
You should follow the above principle with your tax-advantaged accounts as well, but if you have IRAs at more than one institution, be sure that your yearly contribution does not exceed the yearly limit across ALL accounts. For example, if you have an IRA at both Vanguard and Fidelity and the yearly contribution limit is $5000, you can't contribute $5000 to each of them--you can only contribute $5000 total.