It appears from the photo that you have a slight crack in or near the joint where the headstock meets the neck. This is typically the weakest part of a guitar neck. Many guitars have a separate piece of wood from which the headstock is carved and it is joined to the neck with a glue joint. But it is also where the neck get's thinnest to allow for the angle of the headstock.
It is common for guitar headstocks to break during flights on an airplane. It used to be thought (and some still believe) that changes in the atmospheric pressure/air temperature during flight (combined with string tension) was a contributing factor to this but the truth is that most damage occurs due to rough handling by the baggage handlers.
It is recommended that when you ship a guitar, that you support the headstock inside the shipping box or case by stuffing packing material around it, filling all the voids, so it is stabilized. A sudden jolt to a guitar neck due to something like tossing the case into a luggage hold - could easily crack or snap an unsupported headstock.
If you have not already done so, you might want to seek some relief for the damage if it occurred during shipping, or from the original seller if he/she failed to disclose the damage.
If applying pressure to the cracked headstock causes it to open slightly (get a little larger) it can be repaired by injecting the right type of glue into the crack with a hypodermic needle and then clamping it. Or for a larger crack, you can push the glue in with a stiff piece of paper or plastic film.
There are tons of videos like this one How to repair a cracked headstock on YouTube which show different ways of repairing cracked headstocks and guitar necks. But unless you are very handy with tools, you might want to have an experienced guitar repair technician or luthier make the repair for you.
If the crack does not seem to move or open up when you flex the headstock, it might be fine to just play the guitar and hope for the best. Maybe you use this guitar for a drop or flat tuning to put a tad less string tension on the neck and it might help prevent the crack from getting worse.
If you do notice it starting to get worse, it is probably best to get it repaired before it breaks completely off. Although even if it breaks completely off the neck, it can still be repaired. And the good news is, with the right glue, the repair is likely to be stronger than the original wood.