Skilled picking usually leaves a lock working, because it moves the parts inside the way the key would. Amateur attempts with the wrong tools can break springs, wear parts down or leave a snapped pick in the keyway. Drilling and snapping are different: they destroy the cylinder, which then has to be replaced.
Picking works the pins inside a cylinder into the position the right key would put them in. Done by someone trained, with proper tools and a light touch, nothing is broken and your existing keys still work afterwards. One locksmith guide notes that a picked lock may show no visible damage at all, which is also why picking is used for non destructive entry.
The risk comes from inexperience. Guides on picking list the ways it goes wrong: broken springs, worn internal parts and picks snapped off inside the keyway. Improvised tools such as hairpins and screwdrivers tend to make all of these more likely, and one locksmith guide warns that a lock forced open without the right tools may no longer work properly, leaving the door unprotected.
Some locks are built to resist picking. High security cylinders use pins and other features designed to defeat it, and the Master Locksmiths Association says that when a locksmith gets no feel in a lock while picking or bypassing, it may need to be drilled. A lock whose mechanism has failed, or that has been attacked and is fully locked, can leave drilling as the only route too.
Drilling and snapping always cost you a cylinder, which is why the MLA expects a locksmith to try non destructive methods first. There is one case where drilling can make sense from the start: if your keys are lost and the lock is being replaced anyway, the MLA notes that drilling the old one is acceptable, since it is coming out regardless.
