ほしい means "(I) want (something)". It is an -adjective and conjugates as such. The object of desire is usually followed by the particle が. In negative sentences, the particle はis also used.
Ex: いい漢字のじしょがほしいです。(I want a good kanji dictionary)
ほしい is similar to たい, in that its use is primarily limited to the first person, the speaker. These words are called "private predicates", and they refer to the inner sensations which are known only to the person feeling them. Therefore, one must use extra devices for sentences with private predicates as applied to the second or third person.
Ex: ロバートさんはコンピュゥターがほしいと言っていました。（Robert says he wants a computer)