Thanks both of you for the suggestions! Honestly, some of the responses left me with more questions, such as "Blue/green sharpness? Wha?" and "What changes were made between Tri and Ultimate that I should be aware of?" but I'll do some research before I come back with more!
I appreciate people being so friendly here. It's a nice break from the usual bickering in other threads.
The sword under your health and stamina bar shows you what sharpness your weapon has currently. Early game weapons start with a maximum sharpness of yellow (designated on the HUD with no color), and as you use them, they go down to orange and red. You resharpen the weapon with a whetstone.
As you upgrade your weapons, you'll begin to get better sharpnesses. From worst to best, the sharpnesses are: red, orange, yellow, green, blue, white, purple. Yellow is in the middle of the road, with a damage multiplier of 1.00. Orange and red deal less damage and bounce off of body parts more. Green, blue, white, and purple deal more damage and are less likely to bounce. Purple sharpness will slice through almost anything.
In Tri, Barroth was the first monster to punish you if you didn't grasp the concept of sharpness since he has tough skin. It's highly suggested you have a weapon with at least green sharpness when fighting him.