Skill books give you a free skill point, which you can use for any skill that you meet the level requirement for; Lockpicking is just useful in Farglow to get the other chest.
If you have skill points, there will be a small arrow tab under the skill icon, on the right of the circle showing the skill level; click on that to add a skill point, and another left arrow tab will appear on the left, allowing you to remove the point, and Accept and Revert buttons will show up on the bottom right corner of the skill window which you use to apply or cancel your skill point allocation.
There are indicators for having free skill and stat points. Initially they can be a useful reminder that you have leveled up (ie if it was in the heat of battle you may have missed it), but eventually you'll want to at least save up skill points until you reach level requirements, etc (ie there are probably a couple you'll want to get at level 15), so you'll get used to the icon(s) always being there and ignore them.