I'm no expert, but it gets there because of the localized extreme heating during welding. Thermal expansion works into the cold material and the stress is retained in base metal. Its good to remove it because metal under stress is suseptible to all kinds of solute effects concetrating undesirable interstitials as well as vancancies. But basically you are trying to make one nice homogeneous part and now you have a base metal, stressed metal and then a weld and each has different properties making design more difficult.

I could be wrong. Others please correct me.

Imagine a piece of metal with a small circular melted zone in the center. As the melted part cools there will come an instant when the last bit solidifies. At that instant that bit is as expanded as it can get as a solid and contains essentially no stress. As it cools further it tries to shrink, however it is surrounded by cooler and hence stronger material so it cannot shrink. Therefore since the metal cannot move to be the size it wants to be a stress appears, often as much as the yield stress of the material.
Bill

Vibrational Residual Stress Relief
A AWS welding research supplement published in the Feb. 1976 Welding Journal contained a rather extensive desertation on welding residual stresses and the use of resonant vibrations as a means to reduce them. The supplement was titled: Vibrational Residual Stress Relief in a Plain Carbon Steel Weldment .
Discussed was the method of introducing residual stress and graphical results. Also noteworthy is the graphical results comparing welded ( not vibrated ) samples vs. welded ( vibrated ) samples. An excellent begining reference.