Mutagens are special objects that make Geralt stronger. Similarly to skills, they must be placed in specific slots in character window. Red mutagens focus on increasing attack strength, blue mutagens increase witcher signs' effectiveness and green mutagens increase the size of Geralt's health bar.
There are only four mutagen slots and, just as in case of skill slots, not all are available from the beginning (you must reach level 28). What's important, mutagens can "cooperate" with your skills. It happens when you combine a mutagen and a skill of the same color in one group of slots. An example of such combination can be seen on the picture above - adding three red skills (Fencing category) to red mutagen has greatly improved its effectiveness. Of course, you don't need to combine colors no matter what, but the more connections you manage to create, the better it is for Geralt.
Mutagens can be obtained mostly by killing monsters and checking their corpses (the best mutagens can be found in monsters from witcher contracts). You can prepare them on your own based on alchemy as well - few low level mutagens can be used for creating one higher level mutagen.