Why might a business invest in another company's stock?

A major reason for one firm to buy the stock of another
firm is as a means to move towards merging with or acquiring that
company.

It is not unusual for two firms to merge or for
one to acquire the other.  Firm A, for example, might believe that it can make more
money if it acquires Firm B.  It might believe that it can acquire Firm B, fire many of
its workers (by getting rid of people who are duplicated in Firm A's work force), and
still produce as much revenue as A and B together used to
produce.

As a step towards acquiring Firm B, Firm A would
typically try to buy up as many of Firm B's shares as it could.