Buy, purchase mean to acquire something for money or an equivalent.
Buy is at once the more general and the homelier word; consequently, while it may be freely used of any such transaction, it is distinctly the word of choice in respect to small, casual, or day-to-day exchanges of money for goods. Purchase, on the other hand, frequently implies a transaction of some dignity or importance and negotiations or other efforts to obtain it.
Thus, one buys (rather than purchases) a dozen eggs, a glass of beer, or a new hat, but one purchases (or buys) a yacht or a country estate.
Whereas buy may almost always be substituted for purchase without disadvantage, the use of purchase instead of buy often weakens the effect or strikes a jarring note.