The lawn mower that is broken is in the garage. (Tells which one)
The lawn mower, which is broken, is in the garage. (Adds a fact about the only lawn mower in question)
The use of which for that is common and written and spoken language (“Let us now go even unto Bethlehem, and see this thing which is come to pass.”) Occasionally which seems preferable to that, as in the sentence from the Bible. But it would be a convenience to all if these two pronouns were used with precision. The careful writer, watchful for small conveniences, goes which-hunting, removes the defining whiches, and by so doing improves his work.
William Strunk, Jr. and E.B. White