Past tense of "want to enter"
入る enter
入りたい want to enter
入りたかった wanted to enter
It is used to modify the following noun in the example you gave. This construction is, in terms of function, akin to relative pronoun clauses in English.
Examples:
乗りたい電車 (noritai densha) (The train which I want to ride)
見た映画 (mita eiga) (The movie which I saw)
見ていた映画 (mite ita eiga) (The movie which I was watching)
A very simple and extremely useful construction. Learning it will do wonders for broadening the range of ideas you are able to express in Japanese.