To start with, it could actually be your prostate. The prostate can grow towards the front part of the gland. But the back part of the gland can feel normal. This is the part the doctor can feel during a digital rectal exam.
Even if only the front of the gland is slightly enlarged, it can put pressure on the tube (urethra) that carries urine out from the bladder. If this happens, you will have a more frequent urge to urinate.
Other reasons for the need to urinate at night:
Simply drinking too much water or other fluid.