1.
wanted, desired
Used to express that you want something (a noun). The thing wanted is marked with が.
When I was a child, I wanted a dog, but I couldn't have one because my house was small.
Past tense: 欲しかった
2.
to want (someone) to do
In the pattern 「～てほしい」, expresses wanting someone else to do something.
欲しい conjugates as an i-adjective: 欲しくない (negative), 欲しくて (te-form), 欲しかった (past). Important: Use 欲しい for wanting things (nouns), but use ～たい for wanting to do actions (verbs). The pattern ～て欲しい means you want someone else to do something.