Blood vessels are basically organic tubes that the blood travels through. Blood pressure describes the force with which the blood is passing through the tubes and simultaneously pressing against the walls, which is based on fairly simple mechanical elements such as the diameter of the tube, the volume of blood, and the heart rate. Blood pressure is a highly dynamic system involving many different factors, and blood vessels are equally subjected to, and influential upon, the blood pressures the system experiences.
The main issue with blood pressure and regulation is that low blood pressure (hypovolemia) can lead to shock due to insufficient tissue perfusion; basically there isn't enough blood reaching the body to supply the demand. The opposite, high blood pressure, is potentially more dangerous because it can cause physical damage or destruction to the blood vessels. Both conditions can lead to life-threatening situations such as stroke or aneurysm.
Adaptation to blood pressure changes is necessarily a complicated system, and there are a wide variety of ways in which the body can influence it via the blood vessels, ranging from top-down signals from the nervous system to bottom-up changes resulting from pressure or solute action influencing the vessel cells directly. Ultimately, most blood pressure adaptation at the level of the vessels involves a change in the diameter of the vessels; vasoconstriction (getting smaller) and vasodilation (getting larger). This is accomplished by virtue of the fact that the vessels are partly composed of smooth muscle cells.
So, in short, the vessels can adapt to blood pressure changes by either relaxing or constricting, depending upon the change they experience and the many other factors being fed to the vessels at any given time—for example, factors released by the endocrine system counteracting what would otherwise be a homeostatic change. One way in which a vessel could completely self-regulate would involve the use of mechanosensitive ion channel receptors—basically, a means of recognizing physical stress being placed on the cell and triggering a change in intracellular ion concentrations, which would lead to the appropriate constriction or dilation response.