I found the following image, and would like to know where it is referring me. What does the line across it mean?
Working from information Robert Hoare provided in his answer, I found Ancestry.com has two similar, but not identical, collections that include New York's index to naturalization records. The earlier 2007 digitized collection is titled, "New York, Index to Petitions for Naturalization filed in New York City, 1792-1989." The later instance is part of a much larger collection (2010) titled, “U.S. Naturalization Record Indexes, 1791-1992 (Indexed in World Archives Project).”
In the earlier digitized collection, I located what seemed the entry/image GeneG had uploaded as part of this question. It cites a particular NARA Northeast Region collection "Soundex Index to Petitions for Naturalization filed in ... New York City, 1792-1989." In this particular digital collection, the 2007 version of the card was indexed as "Michael Dresher."
I searched the Ancestry index for this 2007 digital collections several times; even browsed images, but was unable to find the second referenced card. (Might my soundex be rusty?)
In the more recent digitized collection, I was able to locate the two different cards/entries that seem the same records Robert Hoare found. Graphic below from Ancestry's database, "U. S. Naturalization Record Indexes, 1791-1992 (Indexed in World Archives Project"; cites NARA micropublication/microfilm serial M1674, "Soundex Index to Petitions for Naturalizations Filed in Federal, State, and Local Courts in New York City, 1792-1906," roll 64.
The upper card, which seems more complete, probably appears first on the roll (Ancestry's images 3500-3501); indexed as "Michael Dresouer"). The lower card (images 3502-3503) was indexed as "Michael Dresuer."
Presumably Volume 38 is a bound volume of naturalization records in the City Court of Brooklyn, and the record of Michael Dresuer was numbered as record 224 in that volume. Your next step is to write to the court with the 38/224 info and ask for a full copy of that record. They may write back and say it has been archived somewhere else and provide you with that info.
The line is labelled as "see" so it is simply referring you to the original record if you want to know who were the witnesses.
In that image set, there are two cards with that "copy of record no", the one you've shown, and another one that is two images earlier in the set. None of the other images have the same "copy of record no".
The second image has all the normal details that appear on these cards, and almost the same last name as the image in the question. So it appears that the "<-- See -->" on the image means see the other card with the same number, as that is where the information is to be found.
To put it another way, the card above is a cross-reference card with an alternative name spelling, and it is pointing you to the other more complete card.
The more complete card is the other card with the same record number (that's what links them). The card for Michael Dresouer, on image 3500. That gives details like the date and witness. Looking at other records, it's likely that that is all that was on the original.
On this site displaying a similar image, you will read
If that is correct, you will not need to refer back to the court because these are NARA reference numbers that can be used directly.
The form itself is intriguing. A Google Image search correctly identifies it as a Naturalization Record, but among the dozens of images considered visually similar this not a very common type. It seems to have been used only in NYC and is distinguished by NOT having the names of any Federal Agencies on it. (Other types are clearly Dept of Labor INS). My guess is that this was a locally produced index card to reference records that had been taken away from the place they were created.