An ingrown toenail has a plain definition: the nail grows into the skin beside it. The useful question is what pushes it there, and the published answers are more specific than most people expect.
Two causes named in print
First, the trim. MedlinePlus says toenails trimmed too short, or with the edges rounded rather than cut straight across, may cause the nail to curl and grow into the skin.
Second, the shape of the nail. Cleveland Clinic says that if the toenail curves with the shape of your toe, it can grow into your skin.
Notice the difference. One cause is about how the nail is cut. The other is about how the nail is shaped.
Where to read the details
For descriptions of the condition and what follows it, see the MedlinePlus entry on ingrown toenails, the MedlinePlus discharge instructions after ingrown toenail removal, the Cleveland Clinic page on signs, causes, treatment and prevention and the NHS page on ingrown toenail.
What to confirm, and with whom
If you have had the same toe go bad more than once, ask your podiatrist whether your case looks like a trimming problem or a nail-shape problem. Ask what that answer means for your next step.
The clause people skip
"Straight across" is an instruction with two parts: no rounded corners and not too short. Following only one of them leaves the other cause in play.