This particular that (there are several others) is being used to mark and introduce a tensed complement (often called simply a That-Complement). Such words are called Complementizers, like the for...to of many infinitive complements.
- I think that [I shall never see a poem lovely as a tree].
- I said for [him to ask his mother about it].
Under certain circumstances complementizers may be deleted. For instance, for is not normally used before subjects of infinitives:
- I told him to ask his mother about it.
- *I told for him to ask his mother about it.
and that is often dropped before a tensed complement, if it is clear that it's a complement. This condition is usually met simply by using the clause as object of an appropriate verb, so that is probably dropped more frequently than not -- unless it's needed for rhythmic purposes, as in the first sentence above, which comes from a famous American poem.
However, if the complement is the Subject of a verb instead of its Object, that can't be dropped, because a subordinate clause at the beginning of a sentence needs to be marked as being subordinate:
- That he came to the party is surprising.
- *He came to the party is surprising.
So Christi has it right on. One can leave it in or leave it out, and it means the same, and is equally grammatical, either way. Lots of things in English syntax work like that.