To make sure it actually is blood, and (in some cases) identify what type of blood it is / informal blood spatter anyalysis
As noted in TV Tropes entry,The Ketchup Test is where:
a character touches a blood stain with his fingers, usually in order to make sure that it actually is blood.
Sometimes, it turns out to be ketchup or strawberry jam (something that's red, goopy and fake), especially if another character has been doing a Chicken Little impersonation over the supposed bloodstain.
Being a vampire or a cyborg may also help for analysing the type of blood. In Real Life, it's possible that some animals (bloodhounds, brown bears, tyrannosaurs, larger sharks) may have a sufficiently powerful sense of smell, this (or simply sniffing the blood) might actually allow them to determine the species or even the individual victim involved.
See also Sniff Sniff Nom, Fingertip Drug Analysis.
There are plenty of examples on the above links of charcters who use the taste-test as a way of furthering their understanding of a situation.
It could also be that touching the blood allows the character to identify any clotting, which can help identify how long ago the blood came into contact with the surface, and from what part of the body:
Blood is in a liquid state when inside the body, and when it exits the body, it does so as a liquid. But as anyone who has had a cut or a scrape knows, it doesn’t remain a liquid for long. Except for people with hemophilia, blood will begin to clot within a few minutes, forming a dark, shiny gel-like substance that grows more solid as time progresses.
The presence of blood clots in bloodstains can indicate that the attack was prolonged, or that the victim was bleeding for some time after the injury occurred.