Vanguard Brokerage Services
This article explains the distinction between the Vanguard mutual funds and Vanguard Brokerage Services.
Many investment companies are really several interlocked businesses operating under one marketing name. With "Vanguard" you need to understand the difference between The Vanguard Group and Vanguard Brokerage Services (VBS).
The Vanguard Group operates Vanguard mutual funds--the ones with "Vanguard" in their name, Vanguard Total Stock Market Index Fund, Vanguard Wellesley Income Fund, and so forth. (The Vanguard Group has a unique "mutualized" governance structure but we won't go into that here).
Vanguard Brokerage Services (VBS) is a brokerage like any other. At VBS you can can buy an individual stock, such as Apple stock or WisdomTree Total Earnings ETF; an individual bond, such as a treasury bond or a bank CD; or a mutual fund, such as Fidelity Contrafund. If approved by VBS, you can even trade option contracts  or open a margin account. 
Buying mutual funds directly
You do not need a brokerage in order to invest in mutual funds. At The Vanguard Group, as at most mutual fund companies, you can open up an investment account directly with the mutual fund company. That account is not at a brokerage like TD Ameritrade or E*Trade , it is at The Vanguard Group, or Dodge & Cox, or MFS, and you get statements and such from the mutual fund company itself.
Of course, if you have an account directly at a mutual fund company, you can only buy that company's own mutual funds, unless the mutual fund company also operates a brokerage.
If you have a specific commitment to a specific mutual fund family that will be the core of your investments, investing directly with the fund company is often a good choice. They tend to treat you nicely and often provide some small benefits. For example investing directly at Vanguard gives you access to lower-cost Admiral shares of the popular index funds. Thus, if you have a major commitment to Vanguard mutual funds as the core of your investment portfolio, there is a good case to be made for opening an account directly with Vanguard.
Vanguard Brokerage Services
Many but by no means all of the larger fund companies also offer general brokerage services. Vanguard Brokerage Services is a separate business under the same roof as The Vanguard Group. This is true at other companies, although with some companies the mutual funds and brokerage are so seamlessly joined that you may not even realize that more than one business is involved. At Vanguard, though, you actually need to open a separate account. This is a quick and easy process, but not automatic.
If you want to hold other investments besides Vanguard mutual funds, what are your options? Could you hold your Vanguard Funds at Vanguard and everything else at (say) WellsTrade? Of course, and many sensible people do. The problem is complexity. For example, if you want to buy a Vanguard Fund at Vanguard, the money to buy it needs to be in your Vanguard account, not somewhere else. If it's somewhere else, you first have to move it to Vanguard, the transfer needs to complete, the check needs to clear, etc.
The chief convenience of having everything at Vanguard is that you have a single money market fund account that is common to The Vanguard Group and the account at Vanguard Brokerage Services. Other small conveniences include receiving a single end-of-year tax statement, having the portfolio analysis tools know your whole portfolio automatically, and having your non-Vanguard investments count toward Voyager or Flagship status. 
The quality of Vanguard Brokerage Services is much-discussed in the forum. Opinions include "good" and "OK" and "why should I settle for 'OK' when others are better." If you did not invest in Vanguard products at all, you probably would not choose Vanguard Brokerage Services as your broker. Kiplinger recently gave them good marks in a survey of online brokerages, and their statement probably sums it up best: "Vanguard’s performance on our survey is particularly impressive because the company’s brokerage business exists primarily as a supplement to its mutual fund business, rather than as a standalone service."
- List of the fees and commissions charged by Vanguard Brokerage Services®, Vanguard, Retrieved 31 March 2016.